Social Network Analysis • Project Management • Stakeholder Network Projects Are Inherently Complex, So Are Their Management (Pich, Loch, & Meyer, 2002)

Home , Betweenness centrality, Centrality, Degree (graph theory)

DOI NUMBER: 10.19255/JMPM01310

PROJECT RELATIONSHIP 1.INTRODUCTION KEYWORDS ------Social network analysis • Project management • Stakeholder network Projects are inherently complex, so are their management (Pich, Loch, & Meyer, 2002). the words ‘node’ and ‘actor’ interchangeably. • Network centrality • Community structure This complexity requires collaboration among different relevant entities (e.g., project Social network analysis (SNA) is the map- members and stakeholders) of the project during the completion of its different activi- ping, visualising and measuring of re- ties. The presence of such collaboration leads to the development of various networks lationships among actors in a network among different entities of the project during its completion phase. Understanding (Carrington, Scott, & Wasserman, 2005), the structural characteristics of these networks can reveal important insights (e.g.,reason which, this provides article bothuses visual the and words mathemat- ‘node’ and anthropologists, headed by first Max Gluckman which entity is in the central of the network and which one serves a gatekeeper within‘actor’ ical interchangeably. analysis of networked relations. It has and later by Jams Clyde Mitchell, for exploring the network) that are very crucial for the successful completion of the project (Prell, Socialbeen networksuccessfully analysis applied (SNA) to evaluate is the the mapping , community networks in southern Africa, India and Hubacek, & Reed, 2009). The primary aim of this study is to illustrate how measuresvisualising and measuring of relationships among United Kingdom (Gluckman, 1973; Mitchell, 1966, SOCIAL and methods of social network analysis (SNA) can be used to examine the structuralactors in a network (Carrington, Scott, & 1969). During the era of 1970s, Harrison White and The usefulness of applying SNA to a net- characteristics of such project networks. To achieve this aim, this study explores twoWasserman, workpositional has 2005 in�luencebeen), whichfound of actorsprovidesvery useful in networks. both across visual and his research team produced an amazing number of networks that evolve during the course of the completion of a project among its dif-mathematicalmany disciplines analysis because of networked of its ability relations. to It important contributions such as ‘Block models ferent stakeholders using various methods and measures of SNA. has beenassess successfullystructural patterns applied and to networkevaluate the theory for Social Structure’ to the methodological positional influence of actors in networks. The developments of SNA (Berkowitz, 1982; Mullins NETWORK Although the network analysis approach has long been followed in various research behaviour (Brandes & Fleischer, 2005). usefulness of applying SNA to a network has been & Mullins, 1973; Scott, 1988). According to areas as an advanced and robust technique, it has recently been receiving attention By examining a stakeholder network, for found very useful across many disciplines because Freeman (2004), contemporary network analysis in the project management research (Chinowsky, Diekmann, & O’Brien, 2009). Pre- example, in terms of nodes and their re- of its ability to assess structural patterns and methods and measures could never have emerged viously, this approach had been used as a key approach to address network organi- lationships, an assessment of the impor- network behaviour (Brandes & Fleischer, 2005). without their contributions. In brief, SNA was sation issues in management, particularly network characteristics and their effects tance of the member stakeholders can By examining a stakeholder network, for example, originated in 1930s, had been maturing in empirical ANALYSIS on business organisation (Tichy, Tushman, & Fombrun, 1979). With the rapid devel- be inferred (S. Borgatti, 2005). This will in terms of nodes and their relationships, an research in 1950s-1960s, and in 1970s theoretical opment different network analysis tools, such as UCINET (S. P. Borgatti, Everett, & give the corresponding project manager assessment of the importance of the member research to develop SNA methods and measures Freeman, 2002) and PAJEK (De Nooy, Mrvar, & Batagelj, 2011), the network analysis a deeper understanding about the priori- in Project Management - stakeholders can be inferred (S. Borgatti, 2005). was initiated. ty of different stakeholders, which is very approach has gradually been followed as a key method of hybrid research designThis will give the corresponding project manager a Since its inception in 1934, SNA has been important for the successful completion A case study of analysing to address several important topics in management research, including knowledgedeeper understanding about the priority of different gaining significance in diverse range of research of the project. On the other side, there are transfer and consensus building (Carlsson & Sandström, 2008; Newig, Günther,stakeholders, & which is very important for the areas, including communication studies (Diesner, many SNA tools (e.g., Organisational Risk stakeholder networks. Pahl-Wostl, 2010). In response to this trend, the network analysis approach has successfulre- completion of the project. On the other Frantz, & Carley, 2005), organisational studies Analyser (Carley, 2010)) developed for recently been introduced to the project management research. Since the introductionside, there are many SNA tools (e.g., (Friedkin, 1982), public health (Uddin, 2016) and searchers to visualise relations among ac- there is an increasing trend of the adoption of this approach to the project manage-Organisational Risk Analyser (Carley, 2010)) social psychology (S. Wasserman & Iacobucci, tors in different contexts; for example, the ment research. However, this adoption so far remains at a very initial stage. For thisdevelo ped for researchers to visualise relations 1988), and has become a popular topic of SHAHADAT UDDIN amongcommunication actors in different network contexts among; for the example, team the speculation and study. In project management, it • Complex Systems Research Group, Faculty of Engineering & IT then explore two project networks using those measures and methods. members of a mega project. The ability to reason, this article �irst explains some SNA measures and methods thoroughly andcommunication network among the team members has recently been receiving attention for research • University of Sydney, Australia of a visualisemega project the relations. The amongability a networkedto visualise the analysis purposes. Prell et al. (2009) followed a • [email protected] set of actors and to quantify their structur- 2. SOCIAL NETWORK ANALYSIS relations among a networked set of actors and to SNA approach to analyse stakeholder networks in al importance within the network make ------quantify their structural importance within the natural resource management. Crane (2007) used the SNA very useful to explore many net- A social network can be viewed as a set of actors and a set of links among those actorsnetwork make the SNA very useful to explore SNA methods and measures to understand the worked systems. (S Wasserman & Faust, 2003). In a social network, an actor is a node which repre-many networked systems. multidimensional determinants and complexity of sents an entity, such as individual or organisation. The formation of a social network tobacco use. Similarly, Mok et al. (2017) used is typically associated with the need for an actor to receive some sort of information basic network centrality measures in identifying key challenges in major engineering projects based • ABSTRACT • or resource from others; thus creating an exchange whereby investments of actors in relationships determined by their level of needs. In a visual illustration of a social on stakeholder concerns. There are many other Networks evolve naturally among different relevant entities during the completion of a project. These networks can be of different types; for example, a network, actors are presented by nodes and relations among actors are presented by examples of project management research studies Node Link/Edge where researchers used SNA methods and communication network among project staff or a contact network among project stakeholders. The present literature have documented that a network links or ties. In Figure 1, two nodes are presented by two small circles and a link shows analysis of such networks can provide valuable insights about the structural embeddedness of those networks that are otherwise not revealed and very measures for research analysis purposes (e.g., the relation between them. The two nodes and a link between them form a network. crucial for the successful completion of any group effort. A network analysis can reveal, for example, the relations among actors, how actors are positions Chinowsky et al., 2009; Hagedoorn, 1996; Pryke, Some researcher argued to use the word ‘node’ to represent an objective entity (e.g., within a network and how relations are structured into overall network patterns. This article follows a case study approach to explore stakeholder networks 2004). However, the existing SNA studies of the a webpage in the World Wide Web where two webpages are linked if one of them con- using measures and methods of social network analysis. In doing so, it explains the social network measures and methods that have been used and reports Network present project management research lack of a tains the link of the other) and the word ‘actor’ to represent a subjective entity (e.g., FIGURE 01. Illustration of a social network which has two comprehensive detail regarding how different SNA an individual in a mobile communication network). For this reason, this article usesFigure 1: Illustration of anodes social and networkan edge. which has two nodes the �indings from the case study. and an edge. measures can reveal different meaningful insights about the structural positions of actors within a 106 JOURNAL OF MODERN PROJECT MANAGEMENT • MAY/AUGUST • 2017 The origin of2017 social • JOURNALMODERNPM.COM network analysis 107 (SNA) network. This study presents a comprehensive can be traced back in the early 1930s with the illustration about how different SNA approaches sociometric studies of Jacob Moreno at the Hudson can be used in the context of project management School for Girls (L. C. Freeman, White, & by considering a case study. Romney, 1992; Hummon & Carley, 1993; Leinhardt, 1977; Marsden & Lin, 1982; S 3 MEASURES OF SOCIAL NETWORK ANALYSIS Wasserman & Faust, 2003). Indeed, the year in Over the time researchers proposed various question is 1934, when the book ‘Who Shall social network measures. Some of them Survive’ by Jacob Moreno was published. Clearly, quantify the structural characteristics of the the publication of this book was significant in the complete network while some other emphasise introduction of social network analysis. SNA had the structural influence of individual nodes been further developed regarding its applicability in empirical research with the kinship studies of over the complete network. This section Elizabeth Bott in England during the 1950s (Nadel, discusses only those SNA measures that are 1957) and the 1950s-1960s urbanisation studies of used in the next section to explore the case the University of Manchester group of study.

Page 2 of 9

FigureFigure 3: A star 3: A network star network having having five nodes five nodes where where A is the A is the central node central node B B

Figure 3: A star networkIn the Inhaving network the fivenetwork nodes of Figure whereof Figure A2, is consider the 2, consider the node the node A. A. central node ThenThen we need we need to consider to consider all other all other remaining remaining nodes nodes B C C (i.e., B, C, D and E) and their all possible pairs A A SOCIAL NETWORK ANALYSIS IN PROJECT MANAGEMENT - A CASE STUDY OF ANALYSING STAKEHOLDER NETWORKS In the network(i.e., of FigureB, C, 2,D considerand E) andthe nodetheir A. all possible pairs (i.e., (i.e.,BC, BC,BD, BD,BE, CD,BE, CD,CE, DE).CE, DE). Now Now consider consider the the ' N −1 Then we need to consider all other remaining nodes Cn() = ...... (2) shortest paths for these six pairs. Both BC and CD A C 3.1 NETWORK CENTRALITY AND Ci N (i.e., B, C, D andshortest E) and paths their for all these possible six pairs. pairs Both BC and CD has hasonly only1 shortest 1 shortest path path(i.e., (i.e.,BAC BAC and andCAD, CAD, D D CENTRALISATION dn(,ij n ) (i.e., BC, BD, BE, CD, CE, DE). Now consider the The origin of social network analysis (SNA) can be traced back relaying of information.∑ The following equation representsrespectively) the sider and the Ashortest is within paths those for paths. these Theresix pairs. are Both BC and CD has 3. MEASURES OFCentrality SOCIAL NETWORKis an important ANALYSIS concept in studying j=1 shortest paths forrespectively) these six pairs. and BothA is withinBC and those CD paths. There are in the early 1930s with the sociometric studies of Jacob Moreno ‘closeness centrality’ for a node i in a network having N nodestwo (L. twoshortest onlyshortest paths1 shortest paths for CEfor path (i.e.,CE (i.e., (i.e.,CABE BAC CABE and CADE)andCAD, CADE) respectively) and A is ------different social networks and describes structural has only 1 shortest path (i.e., BAC and CAD, FigureFigure 4: A circle 4: A circlenetwork network having having four nodes four nodes and four and edges four edges or or Freeman et al., 1979; S Wasserman & Faust, 2003): within those paths. There are two shortest paths for CE (i.e., D at the Hudson School for Girls (L. C. Freeman, White, & Romney, properties of a node in a network. On the other and Aand is Awithin is within both bothpaths. paths. On the On other the other side, s tide,here t here links links Over the time researchers proposed various social network meas- Where, the subscript C for ‘closenessN −1’, d(n ,n ) respectively) and A is within those paths. There are 1992; Hummon & Carley, 1993; Leinhardt, 1977; Marsden & Lin, Cn' () = ...... (2)i j are twoare shortesttwoCABE shortest and paths CADE) paths (i.e., and (i.e.,BAD A BADis and within BED)and both BED) for paths. the for the On the other side, side, centralisation describes3.1 theNETWORK structural CENTRALITY AND N −Ci1 N two shortest paths for CE (i.e., CABE and CADE) ures. Some of them quantify the structural characteristics of the ' Figure 4: A circle network having four nodes and four edges or 1982; S Wasserman & Faust, 2003). Indeed, the year in question properties of the entireCENTRALISATION network under is the numberCnCi() of= links in the shortest...... (2)dn(, path n ) between pair pairBD therebutBD Abut are is A withintwo is withinshortest only onlyone paths pathone (i.e., path(i.e., BAD (i.e.,BAD) and BAD) .BED) . for the Thepair ThesetBD of set closeness of closeness centralities centralities (as in (as equation in equation complete network 3.1while someNETWORK other emphasise CENTRALITY the structural AND N ∑ ij and A is within both paths. On the other side, there links consideration. Conceptually,Centrality centrality is anquantifies important concept inactor studyingi and actor j , and the sumj= 1 is taken over all For theFor shortestbutthe Ashortest is withinpaths paths of only remaining of one remaining path two (i.e., twopairs BAD). pairs (i.e., For (i.e., the shortest2), which2), paths which represents represents the collectionthe collection of closenessof closeness is 1934, when the book ‘Who Shall Survive’ by Jacob Moreno was CENTRALISATION dn(,ij n ) are two shortest paths (i.e., BAD and BED) for the how central a node is positioneddifferent in social a network networks ( Sand describes structural ∑ ' BE andBE DE),and DE), A does A does not fall not withinfall within those those paths. paths. indicesindices of Nof nodesN nodes in ain network,a network, can canbe be Centrality is an important propertiesconcept of ina nodestudying in a network . Oni ≠thej .other A higher valuej=1 of C (n ) indicates that pair BD but A is withinof remaining only one twopath pairs (i.e., (i.e.,BAD) BE. and DE), A Thedoes set not of fall closeness within centralities (as in equation section discusses only those SNA measures that are used in 'the N −1 Where, the subscriptC Ci for ‘closeness’, d(n ,n ) the introduction of social network analysis. SNA had been fur- differentWasserman social & Faust, networks 2003 and).side, There describes centralisation areCn three structural() basic=describes the ...... (2)structural Fori jthe shortest pathsthose of remaining paths. two pairs (i.e., summarisedsummarised by the by followingthe following equation equation to measure to measure 3.1 Nin�luenceETWORK of individualCENTRALITY nodes over theAN Dcomplete network. ThisCi N node iWhere,is closer the to subscript other nodes C for of ‘closeness’ the network,, d(n and,n )is the number of 2), which represents the collection of closeness published. Clearly, the publication of this book was signi�icant in next section to explorepropertiestypes the of casecentrality of study. a node measures. in a network properties. Onof thethe otherentire network under is the number of links in the shortest pathi j betweenBE and DE), A does not fall within those paths. the thecloseness closeness centralisation centralisation (L. Freeman(L. Freeman et al.,et al., ther developed regarding its applicability in empirical researchCENTRALISATION dn(, nWhere, )' the subscriptactor i Cand for actor ‘closenessj , and the’, sumd( nis ,takenn ) over all ThusThus, the ,betweennessthe betweenness centrality centrality of A of A indices of N nodes in a network, can be side,Degree centralisation centrality isdescribes one consideration.of basic the measures Conceptually,structural ∑of centralityijC quantifies(nlinks) will in thebe 1shortest when node pathi hasbetween direct actorlinksi withi andj actor j, and the Thus, the betweenness! !! centrality!! !! ! !of A!! ! 19791979): ): C i ' summarised by the following equation to measure with the kinship studies of Elizabeth Bott in England duringCentrality the --is 3.1an NETWORK important CENTRALITY concept ANDin studyingCENTRALISATION how -- central a node is positionedj=1 in a isnetwork the number (S of ilinks≠ j . Ain higherthe shortest value of path C (betweenn ) indicates that ! + !!++!!++!!++!!++!! + ! N N propethe networkrties ofcentrality. the entireFor a networknode, it isunder the N −1 sum is taken over all i j. A higher valueC i of CC(ni ) indicates that 1950s (Nadel, 1957) and the 1950s-1960s urbanisation differentstudies social networks and describes structural Wasserman & Faust, 2003Cn' ()). There= areall three other...... (2) basic nodes of the network. In the network of = = (!!!)(×!(!!!)!×)(!!!) the closeness centralisation ('L. Freeman*' * ' et' al., 3.1 NproportionETWORK of CENTRALITYnodes that are adjacentAND to that nodeCi in N actor i and actor nodej , andi is closerthe sumto other is nodestaken of overthe network, all Thusand , the betweenness centrality of A [CC ([nCC)(−nCC) −(nCiC)](ni )] Centrality is an importantconsideration. concept Conceptually, in studying types differentcentrality of centrality social quantifies measures. node i is closer to other nodes of the network, and CC(ni ) will ! ! ! ! ! ! ! ∑ properties of a node in a network. On the other Figure 2, node A has' a distance of 1 with nodes B, ! 1979): ∑ of the University of Manchester group of anthropologists, headed CENTRALISATIONa network. It highlights the Where,nodeDegree with centralitythe thesubscript mostis one Cof forbasicdn ‘(, closenessmeasuresij n ) of’, will ≠be 1' when node i has direct links with i=1 i=1 networks and describeshow centralstructural a nodeproperties is positioned of a node in in a a networknet- (S ∑ C andbe D 1 since whend(n nodei ,CnodenCj( )nAi )i hashas directdirect connections links with allwith other nodes of the ! + ! + ! + ! + ! + ! N C =C = ………… (5) (5) side, centralisationCentrality describes is an importantthe structural concept in studying j=1 i ≠ j . A higher value of C (n ) indicates that 1 + 01.5++0.05 + 10 + 1 + 01 + 0 C C Wassermanlinks to other & Faust,nodes 2003in a) .the networkThere network are and threecentrality. can basic beFor a node, it is the all other nodes ofC the inetwork. In the network of = (!!!)×(!!!) ' [(* N −[(1N')*−(1N)*−(2N)]−/(22)]N/(−23N) − 3) properties work.of Onthe thedifferent otherentire social side, networksnetwork centralisation and underdescribes describes structuralproportion isthe the structural number of nodes thatof linksare adjacent in the to shortestthem.that nodenetwork. It inhaspath a betweendistance In the network of 2 with of node Figure E since 2, node it can A has a distance of = = [CC (n ) −CC (ni )] defined by the following equation for the node (or node i is closer toFigure other 2, nodenodes A hasof athe distance network, of 1 with and nodes B, ! 6 6 ∑ ploring community networks in southern Africa, India and Unit- properties typesof a node of centralityin a network measures.. On the othera actornetwork. i and It highlightsactor j , theand node the with sumreach the is most Etaken through over the all node D. Therefore, the total i=1 consideration.properties Conceptually, of the entire centrality network quantifies under consideration. Concep-Where, the subscript C for ‘closeness' 1 with’, dnodes(ni ,Cn and j B,) DC sinceand nodeD since A has node direct A connections has direct with connections = 0.58 C = …… (5) by �irst Max Gluckman and later by Jams Clyde Mitchell, for ex- side, centralisationactor) i in adescribes network thehaving structural N nodes (S Wasserman Centralisation Centralisation1 + 0. 5refers+ 0refers +to=1 the0+ .to581 overallthe+ 0 overall cohesion cohesion or orC ' ed Kingdom (Gluckman, 1973; Mitchell, 1966, 1969). During the Degree centrality is one linksof basicto other measures nodes in ofa network anddistanceC' C can(n i )be of will node be them. 1A when with It has nodethe a distance remainingi has ofdirect 2 with nodes links node Ewith( i.e.since it can [(Where,N −1)* (N − 2)]' are/(2 theN − closeness3) indices of N nodes how central a node propeis positionedrties of inthe a networkentire network(S under is the number of links in the shortestwith paththem. between It has a distance of 2 with node E since it can reachintegration E = of a network. A network may, for Where,CnCi() CnCi()are the closeness indices of N nodes the& Faust, network 2003 )centrality.: Fordefined ia≠ node, jby. Athe followinghigherit is the valueequation of for CtheC node(ni ) (orindicates reach that E through the node D. Therefore, the total integration of a network. A network may, for era of 1970s, Harrison White and his research team producedWasserman an & Faust,consideration. 2003). There Conceptually, are three centralitybasic quantifies actor i and actor j , and theB,all sumC,other D is and takennodes E) over isof 5 all the(1+1+1+2). network. Thus, In the the net closenesswork of 6 ' *' * a network (S Wasserman & Faust, 2003). Thereactor) are threei in a network basic having N nodes (S Wassermanthrough thedistance node D. of Therefore,node A with the the totalremaining distance nodes of(i.e. node A example,withexample, Centralisation be morebe more or refers lessor tolesscentralised the centralisedoverall aroundcohesion around or integrationand of is the largest observed value in proportion of nodes thatdn() are adjacentnode i isto closerthat node to otherin nodes of 'the network, and Centralisation refers= 0 .to58 the overall cohesion or andCC (CnC)(n ) is the largest observed value in amazing number of important contributions such as ‘Blocktypes mod- of centralitytually, centrality measures.how central quanti�ies a node ishow positioned central' in aa nodenetworki &is Faust,(positionedS 2003):≠ in. A higher value ofcentralityFigure 2, indicatesnodeof the A node thathas Aa distanceis 0.80 (i.e. of 14/5). with nodes B, ' types of centrality measures. CnDi( )= ...... (1)i j CC the(ni ) remainingB, C, nodes D and (i.e. E) is B, 5 (1+1+1+2).C, D and E) Thus, is 5 the(1+1+1+2). closeness Thus,particular theparticular a network.a node a node or A network a orset a ofset may, nodes.of fornodes. Aexample, network A networkWhere, be more Cn or() lessare cen-the closeness indices of N nodes Wassermana &network. Faust, 2003 It). Therehighlights are three the basic node ' with the most C andBetweenness D since node centrality A has views direct a connections node as being with in integration of a network. A network may, for Ciclosenesscloseness indices. indices. For aFor network a network with withN nodes N nodes, the , the els theory for Social Structure’ to the methodological develop-Degree centrality is one of basic measures of N −1 CC (ni ) node ' willi beisdn closer ()1i when to other node nodesi has of direct the network, linkscentrality withand of the node A is 0.80 (i.e. 4/5). types of centralitylinks measures.to other nodes in a network CnandDi( )can= be ...... (1) closeness centrality of the node A is 0.80 (i.e. 4/5). centralisationcentralisationtralised measure around measure isparticular anis expressionan aexpression node orof a howsetof of how nodes. ' *A network ' athem. favoured It has position a distance Betweennessto theof 2 extent with centrality node that theEviews since node a node it falls can as being example, in be more or less centralised around and is the largest observed value in ments of SNA (Berkowitz, 1982; Mullins & Mullins, 1973;the Scott, network Degree centrality. centralityDegree For is centralityonea node, of basic is oneit measures ofis basicthe measures of the ofnetwork cen- N will−1 be 1 when node i has direct links with CC (ncloseness) closeness centralisation centralisation (i.e. ,(i.e.CC,)C reaches) reaches its its defined by the following equationall other for the CnodesC node(ni ) of (or the network. In the networka favoured of position to the extent that the node falls tightlytightly thecentralisation networkthe network is measureo rganisedis organised is anaround expression around its mostits of most how tightly the net- C proportion of nodes thatthe arenetwork adjacent centrality. to that For node a node, in it is the onreach theBetweenness Eshortest through paths the centrality betweennode D. views otherTherefore, a nodepairs asofthe beingnodes total in particular a favoured a nodepo- or a set of nodes. A network 1988). According to Freeman (2004), contemporary network trality. For a node, itWhere, is the proportionthe subscript of nodes D for that ‘Figuredegree are adjacent ’2, andall node other d A( nodesn has) aof distancethe network. of 1In withthe net nodesworkon oftheB, shortest paths between other pairs of nodes centralcentral point point (S Wa (Ssserman Wasserman & Faust, & Faust, 2003 2003). There)closeness. There indices.maximummaximum For valuea network value of 1 ofwhenwith 1 when Na nodenodes a node chooses, the chooses all other all other proportion actor)of nodesi inthat a are network adjacent havingto that node NWhere, nodesin the (S subscript Wasserman D ifor ‘degree’ andin the network. That is, nodes that occur on many centralisation measurework is isan organised expression around of itshow most central point (S Wasserman a network.to It that highlights node in thea network. node with It highlights the most the node with the mostFigure 2, node A has a distancedistanced sition(ofn i1 ) ofwith tonode nodesthein Aextent B,the with network. that the theThatremaining node is, nodes falls nodes that on occur the (i.e. shorteston many paths be- analysis methods and measures could never have emerged with- a network.indicates& It Faust,highlights 2003the the number) : node with of nodesthe most Cwith and whom D since node nodei is A has direct connections with are threeare three different different types types of centralisation of centralisation that thatclosenessare are centralisation(N-1)(N nodes-1) nodes and (i.e. eachand, C each of) the ofreaches otherthe other (Nits-1) (N nodes-1) nodes has has links to other nodes in a network and can be indicates the numberC and D of since nodes node with A whom hasB,shortest direct C,node D connectionsi isandpaths E) between is shortestwith 5 (1+1+1+2). thepaths other between Thus, pair the of otherthe nodes closeness pair ofhave nodes tightly have the network &is Faust, organised 2003). around There areits threemost different types of centralisation C out their contributions. In brief, SNA was originated in 1930s, links to other nodes in a network and can them.be It has' a distance of 2 with nodetween E since other it canpairs of nodes in the network. That is, nodesbased thatbased on the on three the three basic basic centrality centrality measures. measures. the shortestthe shortest distances distances of length of length 2 to 2the to remainingthe remaining defined by the following equationconnected. for the The node' maximum (ordn ()i valueconnected. for Thethem. maximum It hasis a 1 valuedistance for of 2centralityhigher 'with node isbetweenness 1 Eof since the nodeithigher can cent Abetweenness isrality 0.80 (i.e.than cent 4/5). ralitythose than they those do they central do point (S Wassermanthat are based& Faust, on the2003 three). There basic centralitymaximum measures. value of 1 when a node chooses all other defined by the following equation for the node (orreach EC throughD (ni ) the node D.C DTherefore,(ni ) the total The Theset of set degree of degree centralities centralities (as in (as equation in equation 1), 1), (N-2) actors (i.e., the situation in a star network as had been maturing in empirical research in 1950s-1960s, and in lowing equation for the node (orCnDi (actor) )= in a network ...... (1) havingreach N E through the nodenot D. (Therefore,L.occur Freeman, on the many not total1978 ( L. shortest )Freeman,. The betweenness paths 1978). betweenThe betweenness centrality the other centrality are pairthree of different nodes types of centralisation that are (N-1) nodes and (Neach-2) actorsof the (i.e.other, the(N -situation1) nodes inhas a star network as actor) i in alinks network to other havingactor) nodesi in N a networknodes in a network (havingS Wasserman N and nodes can (S N Wassermanbe− 1de�inedwhen nodeby thei is fol-linked with all other nodesBetweenness in the centrality views a node as being in when node i is linked with alldistance other nodes distanceof node in of Athe node with A withthe theremaining remaininghave highernodes nodes ((betweennessi.e.i.e. ' centrality' than those they do notwhich (L.which representsThe represents set ofthe degree collection the collection centralities of degree of (asdegree indices in equation indices of of 1), whichin Figure inrepre- Figure 3). This3). Thisindex index can canattain attain its minimumits minimum 1970s theoretical research to develop SNA methods and meas- nodes (S Wasserman& Faust, 2003 )&: Faust, 2003): network. For an isolate node, its valuea favoured is 0. In positionfor ato node the nextenti (i.e. CthatB(ni )the) can node be represented falls based by on the three basic centrality measures. the shortest distances of length 2 to the remaining & Faust, 2003): B, C, D and E) is 5 (1+1+1+2).for a Thus,node the n closenessi (i.e. C B(ni )) can be represented by N nodes in a network, can be summarised by the value of 0 when lengths of the shortest distances network. For an isolate node,B, itsC, Dvalue and E)is 0.is 5In (1+1+1+2). Thus,Freeman, the closeness 1978).the following The equation (S Wasserman &for Faust, a node n (i.e.,N nodessents inthe a collectionnetwork, canof degree be summarised indices of Nby nodes the in a network,value of 0 when lengths of the shortest distances ures was initiated. ' dn()i Figure 2, thecentrality node A ofhas the three node connections A ison 0.80 the (i.e. with shortest 4/5). paths betweenbetweenness other pairs centrality of nodes The set ofi degree centralities (as in equation 1), (N-2) actors (i.e., the situation in a star network as ' dn()i FigureCn( ) =2, the ...... (1) node A has threecentrality connections of the nodewith A is 0.80the (i.e. following 4/5). equation (S Wasserman & Faust, followingfollowing equation equation to tomeasure measure the thedegree degree are allare equal all equal (i.e. , (i.e.the , situationthe situation in a incomplete a complete graph graph Where,Di the subscript D for nodes‘degree B, C’ andand D.Betweenness Sinced(n ithere) centralityare five nodes views in a thenode as being2003 in) : which represents thecan collection be summarised of degree byindices the following of equationin Figure to measure3). This theindex can attain its minimum CnDi( )= ...... (1)N −1 in theC Bnetwork.(ni )) can Thatbe represented is, nodes that by the occur following on many equation (S Wasser- N −1 nodes B, C and D. Since therenetwork, are Betweennessfive the nodesdegreea favoured centralityin centrality theposition of Ato willviewsthe2003 extentbe 0.75a )node :that (3/ the as node being falls in centralisationcentralisation (L. Freeman (L. Freeman et al., et 1979 al., 1979): ): as in Figure 5). Thus, indicates the varying indicates the number of nodes with whom node i is shortestman paths & Faust, between 2003): the other pair of nodes have N nodes in a network,degree can centralisation be summarised (L. Freemanby the et al., 1979):value of 0 whenas lengths in Figure of the 5). shortest ThCus,C CdistancesC indicates the varying network, the degree centrality(5 -aof1) favoured =A 0.75). will on be positionthe 0.75 shortest (3/ to paths the extentbetween thatother the pairs node of nodes falls g jk (ni ) in diverse range of research areas, including communication Where, the subscript D for ‘degree’ and d(n ) ' higher betweenness centrality than those they do following equation to measure the degree are all equalamount (i.e., the of situationthe centralisation in a complete of closeness graph compared Where, the subscriptconnected. D for ‘degree’ The maximumand d(n )indicates value i for the C num-in the(n network.) is 1 That is, nodes that occur on many ∑ g N amount of the centralisation of closeness compared Since its inception in 1934, SNA has been gaining signi�icance (5-1) = 0.75). i on the shortestD i paths between other pairs of nodes g' jk (ni ) j

amount of the centralisation of closeness compared N * to star and complete networks. [C (n ) −C (n )] ∑ D D i C = i=1 ………… (4) D [(N −1)*(N − 2)]

Where, CnDi()are the degree indices of N nodes * and CD (n )is the largest observed value in the degree indices. For a network with N nodes, the

degree centralisation (i.e., CD ) reaches its maximum value of 1 when a node chooses all other

(N-1) nodes and the other (N-1) actors interact only Figure 5: A complete network where each node is connected with this actor (i.e., the situation in a star network with all other remaining nodes in the network as in Figure 3). This index attains its minimum value of 0 when all degrees are equal (i.e., the The set of betweenness centralities (as in situation in a circle network as in Figure 4). Thus, equation 3), which represents the collection of betweenness indices of N nodes in a network, can CD indicates the varying amount of the centralisation of degree compared to both star and be summarised by the following equation to circle networks. measure the betweenness centralisation (L. Freeman et al., 1979):

Page 4 of 9

N Figure 6: Illustration of the community structure in an abstract ' * ' network which has three communities (i.e., C1, C2 and C3) [C B (n ) −CB (ni )] ∑ C = i=1 …………. (6) B (N −1) 3.3 COMMUNITY STRUCTURE A network is said to have a ‘community structure’ N if theFigure nodes 6: Illustration of that of the network community structurecan easily in an abstract be divided ' * ' network which has three communities (i.e., C1, C2 and C3) ' [C B (n ) −CB (ni )] Where, CnBi()are the ∑betweenness indices of N into sets of groups such that each set of nodes is i=1 ' * C B = …………. (6) densely connected internally but sparsely nodes and is the largest(N − 1observed) value in 3.3 COMMUNITY STRUCTURE CB (n ) connectedA network externally. is said to have Each a ‘community set of nodes structure’ is called a the betweenness indices. Freeman (1978) ‘communityif the nodes’. of In that the network network can ofeasily Figure be divided 6, there are Figure 3: A star network having five nodes where A is the demonstrates Where,that betweennessCn' ()are the betweennesscentralisation indices of N into sets of groups such that each set of nodes is central node Bi three communities (i.e., C1, C2 and C3). Any node B ' * densely connected internally but sparsely reaches its maximumnodes and value C (ofn )1is for the largestthe star observed graph. value in of these communities has more links with other Its minimum value of 0 occursB when all actors have connected externally. Each set of nodes is called a In the network of Figure 2, consider the node A. the betweenness indices. Freeman (1978) nodes‘community of the’. sameIn the networkcommunity of Figure compared 6, there are with the exactly the samedemonstrates betweenness that index. betweenness centralisation numberthree communitiesof links (i.e.,with C1, otherC2 and C3).nodes Any fromnode other The required network analyses for this case University (Carley, 2010). The second one is Then we need to consider all other remaining nodes C (i.e., B, C, D and E) and their all possible pairs A 3.2 NETWORK DENSITYreaches its maximum value of 1 for the star graph. communities.of these communities This method has more is links used with to other conduct a study have been conducted using two software NodeXL which is a network analysis and Figure 3: A star network having five nodes where A is the Its minimum value of 0 occurs when all actors have tools. The first one is Organizational Risk Analyzer visualisation software package for Microsoft Excel (i.e., BC, BD, BE, CD, CE, DE). Now consider the Density is a network-level SNA measure. The groupnodes-level of the analysissame community of the compared underlying with the social central node B exactly the same betweenness index. (ORA) which was developed by the Center for (Hansen, Shneiderman, & Smith, 2010). density of a network represents the proportion of number of links with other nodes from other shortest paths for these six pairs. Both BC and CD 3.2 NETWORK DENSITY network. In the network of Figure 2, consider the node A. existing ties (or, links) relative to the maximum communities. This method is used to conduct a Computational Analysis of Social and has only 1 shortest path (i.e.,Then weBAC need andto consider CAD, all other remaining nodes D Density is a network-level SNA measure. The group-level analysis of the underlying social C number of possible ties among all nodes of that Organizational System of the Carnegie Mellon respectively) and A is within (i.e.,those B, paths. C, D and There E) and are their all possible pairs A density of a network represents the proportion of 4 networkSTATE. TOBACCO CONTROL PROJECTS IN THE network (S Wassermanexisting ties & Faust,(or, links) 2003 relative). The to densitythe maximum two shortest paths for CE (i.e.,(i.e., CABE BC, BD, and BE, CADE)CD, CE, DE). Now consider the UNITED STATES - A CASE STUDY OF NETWORK The required network analyses for this case University (Carley, 2010). The second one is shortest paths for these six pairs. Both FigureBC and 4: CD A circle network having four nodes and four edges or value for a networknumber is 1of only possible when ties allamong nodes all ofnodes that of that and A is within both paths. On the other side, there ANALYSIS4 STATE TOBACCO CONTROL PROJECTS IN THE study have been conducted using two software NodeXL which is a network analysis and has only 1 shortest path (i.e., BAC linksand CAD, SOCIALD NETWORK ANALYSIS IN PROJECT MANAGEMENT - A CASE STUDY OF ANALYSING STAKEHOLDER NETWORKS network are connectednetwork ( Swith Wasserman each other& Faust, (i.e., 2003 in). The the density NITED TATES CASE STUDY OF NETWORK tools. The first one is Organizational Risk Analyzer visualisation software package for Microsoft Excel are two shortest paths (i.e., BADrespectively) and BED) and A foris within the those paths. There are ThisU caseS study- Ahas been considered from the value for a network is 1 only when all nodes of that (ORA) which was developed by the Center for (Hansen, Shneiderman, & Smith, 2010). two shortest paths for CE (i.e., CABE and CADE) case of a complete network as in Figure 5). On the articleANALYSIS published by Crane (2007). The network pair BD but A is within only one path (i.e., BAD). The set of closenessFigure 4: A circle centralities network having (as four innodes equation and four edges or network are connected with each other (i.e., in the Computational Analysis of Social and and A is within both paths. On the other side, there other hand, for a completely sparse network, the This case study has been considered from the For the shortest paths of remaining two pairs (i.e., 2), which representslinks the collection of closeness case of a complete network as in Figure 5). On the analysis data reported in this case study came from Organizational System of the Carnegie Mellon are two shortest paths (i.e., BAD and BED) forThe the set of closeness centralities (as in equation 2), which repre-densitynected value with is 0, each which other indicates (i.e., in there the case is no of lina completek networkarticle published by Crane (2007study). The came network from two large-scale multistate BE and DE), A does not fall withinpair BD those but A ispaths. within only one path (i.e., BAD). other hand, for a completely sparse network, the twoanalysis large data-scale reported multistate in this case projects study came tofrom evaluate indices of N nodesThe set inof closenessa network, centralities can (as in beequation exists between any two nodes of that network. For For the shortest paths of remaining twosummarised pairssents (i.e., the by collection 2),the which following representsof closeness equation the collectionindices to measure of of N closeness nodes in a network, as in Figuredensity 5). On value the is other0, which hand, indicates for athere completely is no link sparsetobaccotwo net- large control-scale multistateprograms. projects projectsThese to projectsevaluate to evaluate were tobacco control pro- BE and DE), A does not fall within those paths. indices of N nodes in a network, can be an undirected networkexists between of size any N two, theoretically nodes of that network.there For the cancloseness be summarised centralisation by the(L. followingFreeman equationet al., to measure the work, the density value is 0, which indicates there is noconducted linktobacco ex- controlby theprograms. Centre These grams.for projects Tobacco These were projects Policy were conducted by Thus, the betweenness centrality of A summarised by the following equation to measure an undirected networkN of size N, theoretically there Researchconducted of bythe the Saint Centre Louis for UniversityTobacco Policy School of ! ! ! ! ! ! 1979closeness): centralisationthe closeness centralisation (L. Freeman (L. et Freeman al., 1979): et al., are [istsN *between(N −1)] any/ 2 two (i.e. nodes, C 2of) thatpossibleN network. links For an undirected the Centre for Tobacco Policy Research of Thus, the betweenness centrality of A are [N *(N −1)]/ 2 (i.e., C ) possible links Research of the Saint Louis University School of ! + ! + ! + ! + ! + ! ! ! ! ! ! ! N 1979): network of size N, theoretically there2 are [N*(N-1)]/2 (i.e.,Public NC ) Health and had beenthe Saintfunded Louis by University the School of Public (!!!)×(!!!) ! + ! + ! + ! + ! + ! ' * N ' among its N nodes. If there are Nt links among its Public2 Health and had been funded by the = = (!!!)×(!!!) [C (n ) −C (n' )]* ' among its N nodes. If there are Nt links among its American Legacy Foundation and the Chronic C C[CC (in ) −CC (ni )] possible links among its N nodes. If there are N links amongAmerican its Legacy Foundation Healthand1 the andChronic had been funded by the American ! ! ∑ ∑ N nodes in that network, then, mathematically, t 1 i=1 i=1 N nodes in that network, then, mathematically, DiseaseDisease Directors Directors Ass Associationociation. The. networkThe network data is data is C = CC = …… (5……) (5) N nodes in that network, then, mathematically, density can be Legacy Foundation and the Chronic Disease 1 + 0.5 + 0 + 1 + 1 + 01 + 0 .5 + 0 + 1 + 1 + 0C [(N −1)*(N − 2)]/(2N − 3) density can be defineddensity can as be ( Sdefined Wasserman as (S Wasserman & Faust, & Faust, aboutabout thethe connectivityconnectivity amongamong different different = [(N −1)*(N − 2)]/(2N − 3) 1 = 6 2003): 2003): stakeholdersstakeholders inin twotwo different different statesDirectors states (Indiana (Indiana Association and and . The network data Centralisation6 refers= 0 .to58 the overall cohesion or Where, C (nWhere,) are the' closenessare the closeness indices indices of of NN nodes and C (n* ) 2× N Oklahoma). A connection betweenis aboutstakeholders the connectivityis among different Centralisation refers= 0 .to58 theintegration overall ofcohesion a network. or A network may, for C i CnCi() C 2×DensityNt = t ………………. (7) Oklahoma). A connection between stakeholders is ' ' * de�inedDensity as= (S Wasserman………………. & Faust, 2003): (7) broadly defined and includes face-to-face meeting, Node: 16 Node: 13 example, be more or less centralisedWhere, aroundis the Cn Ci largest()areand observed theC closeness(n ) is value the indices largestin closeness ofobserved N nodes indices. value in For a network NN×−( 1) broadly defined and includes stakeholdersface-to-face meeting,in two different states (Indi- integration of a network. A network may, for C NN×−( 1) telephone conversations and emails. This network (a) Indiana Link: 61 (b) Oklahoma Link: 54 particular a node or a set of nodes. A network' * telephone conversations and emails. This network example, be more or less centralised around with N nodes,closeness the indices.closeness For acentralisation network with N nodes (i.e.,, theCC ) reaches its ana and Oklahoma). A connection between centralisation measure is an expressionand of ChowC (n ) is the largest observed value in data was collected by surveying different Figure 7: Visualisation of stakeholder networks for IndianaNode: (having16 strong political and financial climate) and OklahomaNode: (having 13 weak closeness centralisation (i.e., C ) reaches its The density ofThe the density network of the as network in Figure as in 2 Figure is 0.5 2 (i.e., is 0.5 (2×5)/(5×4) data was collected by surveying different particular a node or a set oftightly nodes. the network A network is organised around itsmaximum most value of 1 when a node choosesC all other (N-1) nodes The density of the network as in Figure 2 is 0.5 stakeholders in these two states in 2002. Each of political(a )and Indiana financial climate). The size of a node in bothLink: networks 61 is proportional(b) Oklahoma to its degree centrality value. Link: 54 closeness indices. For a network with N nodes, the (i.e., (2×5)/(5×4) = 0.5) since it has 5 links among centralisation measure is ancentral expression point (S Waofsserman how & Faust, 2003). andThere each ofmaximum the other value (N of-1) 1 when nodes a node has chooses the shortestall other distances of stakeholdersthese states inwas these rated twoagainst states face-to-facesome incriteria 2002 meeting,for. Each telephoneof conversations Figure 7: Visualisation of stakeholder networks for Indiana (having strong political and financial climate) and Oklahoma (having weak are three different types of centralisation that are (N-1) nodes and each of the other (N-1) nodes has (i.e., (2×5)/(5×4)its =five 0.5) nodes since and itthere has can 5 belinks maximum among 10 links FIGURE 07. Visualisation of stakeholder networks for Indiana (having strong political and fi nancial climate) and Oklahoma (having weak closeness centralisation (i.e., ) reaches its maximum 10 links among these 5 nodes. Density describesfinancial the and political climate. According to this political and financial climate). The size of a node in both networks is proportional to its degree centrality value. tightly the network is organised around its most CC among these 5 nodes. Density describes the general these states was rated againststakeholders some criteria is broadly for de�ined and includes Table 1: List ofpolitical five top and fi nodesnancial climate).having The highest size of a nodedegree, in both closeness networks is proportionaland betweenness to its degree centralitycentrality value. values in Indiana based on the three basic centrality measures. length 2 tothe the shortest remaining distances ( ofN -2)length actors 2 to the (i.e., remaining the situation in itsa five= 0.5)nodes since and it therehas 5 canlinks be among maximum its �ive 10 nodes links and there canrating, be which was conducted in 2002,and emails.Indiana wasThis network data was collected central point (S Wasserman & Faust,The set of2003 degree). Therecentralities (as in maximumequation 1), value (Nof-2) 1 actorswhen (i.e. a ,node the situation chooses in aall star other network as general levellevel of cohesionof cohesion in ain network; a network; whereas, whereas, centralisation financial and political climate. According to this and TableOklahoma 1: List stakeholder of five top networks.nodes having highest degree, closeness and betweenness centrality values in Indiana star network as in Figure 3). This index can attain its minimumamong these 5 nodes. Density describes the general found ‘strong’ for having both bypositive surveying financial different stakeholders in these are three different types of centralisationwhich represents thethat collection are of degree(N indices-1) nodes of andin each Figure of 3 the). This other index (N can-1) attainnodes its hasminimum describes thecentralisation extent to describes which thisthe cohesionextent to which is organised this rating, around which was conducted in 2002, Indiana was and Oklahoma stakeholder networks.Indiana Oklahoma N nodes in a network, can be summarised by the value of 0 when lengths of the shortest distances level of cohesion in a network; whereas, and political climates; whereas, Oklahoma was Rank Indiana Oklahoma value of 0 when lengths of the shortest distances are all equal cohesion is organised around particular focal found ‘strong’ for having bothtwo statespositive in 2002.financial Each of these states was Rank Degree Closeness Betweenness Degree Closeness Betweenness based on the three basic centralityfollowing measures. equation to measure thethe shortestdegree distancesare all equal of length (i.e., the 2 situation to the inremaining a complete graph centralisationparticular describes focal nodes. the Centralisation extent to which and density,this therefore,indexed are as ‘weak’ against these two climate 1 ITPC Degree(1.00) MHPCloseness (0.39) St. BetweennessJoseph (0.05) TUPSDegree (0.92) ClosenessTrust (0.36) BetweennessALA (0.07) (i.e., the situation in a complete graph as in Figure 5). Thus, C nodes. Centralisation and density, therefore, are and political climates; whereas, Oklahoma was 1 ITPC (1.00) MHP (0.39) St. Joseph (0.05) TUPS (0.92) Trust (0.36) ALA (0.07) The set of degree centralitiescentralisation (as in equation (L. Freeman 1), et al., 1979):(N -2) actors (i.e.as, thein Figuresituation 5). Thinus, a starindicates network the as varying C conditions (Crane, 2007). This article first conducts CC cohesionimportant is organised importantcomplementary complementary around measures. particular measures. focal 2 2 SF INSF (0.57)IN (0.57) DOHDOH (0.26) (0.26) ITPCITPC Board Board (0.03)(0.03) LatinoLatino (0.85) (0.85) ACSACS (0.32) (0.32) ACSACS (0.05) (0.05) indicates the varying amount of the centralisation of closeness indexed as ‘weak’ againstand these political two climate.climate According to this rat- which represents the collection of degree indices of in Figure 3). Thisamount index of the can centralisation attain itsof closenessminimum compared nodes. Centralisation and density, therefore, are a node-level SNA in order to quantify the 3 3 AHAAHA (0.570 (0.570 ITPCITPC Board Board (0.22) (0.22) B&GB&G of of ININ (0.03)(0.03) ALAALA (0.39) (0.39) OICAOICA (0.23) (0.23) PWorkzPWorkz (0.04) (0.04) N rated against some criteria for �inancial 4 MZD (0.50) St. Joseph (0.19) Latino Inst (0.03) TulsaHD (0.39) UofO (0.19) Alliance (0.02) * compared toto star and and complete complete networks networks.. conditionsimportance (Crane, of different 2007 )stakeholders. Thising, article which within first wasthe conduct conducteds in 2002, Indiana 4 MZD (0.50) St. Joseph (0.19) Latino Inst (0.03) TulsaHD (0.39) UofO (0.19) Alliance (0.02) N nodes in a network, can be summarised[C ( nby) − Cthe( n )] value of 0 when lengths of the shortest distances important complementary measures. 5 Latino Inst (0.43) B&G of IN (0.16) MZD (0.02) Alliance (0.31) OSMA (0.16) OSMA (0.02) ∑ D D i C1 C2 given stakeholder network. It uses some SNA 5 Latino Inst (0.43) B&G of IN (0.16) MZD (0.02) Alliance (0.31) OSMA (0.16) OSMA (0.02) a node-level SNA in order to quantify the 4.1 NODE-LEVEL the network. Oklahoma State Department of Health following equation to measure= i=1the degree …………are all(4) equal (i.e., the situation in a complete graph was found ‘strong’ for having both positive CD measures to visually distinguish the importance of 4.1 NODE-LEVELTABLE 01. List of fi ve top nodes having highest degree, closenessthe network.and betweenness Oklahoma centrality Statevalues inDepartment Indiana of Health centralisation (L. Freeman et al., 1979):[( N −1)*(N − 2)] importance of different stakeholders within the The stakeholder networks for Indiana and Tobacco Use Prevention Service (TUPS) also has a as in Figure 5). Thus, C indicates the varying different stakeholders within the stakeholder Oklahoma are shown in Figure 7. A linkand connects Oklahoma stakeholderdegree networks. centrality of close to 1 (i.e., 0.92) in the C C1 C2 given stakeholder network. It uses some SNA The stakeholder networks for Indiana and Tobacco Use Prevention Service (TUPS) also has a network. Second, it performs a groupOklahoma-level SNA was to indexed as ‘weak’ against two stakeholders if they have contact with each Oklahoma stakeholder network. Madison Health Where, Cn()are the degree indices amountof N nodes of the centralisation of closeness compared Oklahoma are shown in Figure 7. A link connects degree centrality of close to 1 (i.e., 0.92) in the N Di measuresexplore theto visuallytendency ofdistinguish stakeholders’�inancial the preferences importance and political of climates; whereas, ---other 4.1 at least NODE-LEVEL once per month. --- In this figure, the size Partners (MHP) and Tobacco Settlement and * these two climate conditions (Crane, 2007). two stakeholders if they have contact with each Oklahoma stakeholder network. Madison Health * and C (n )is the largest observed valueto star in theand complete networks. differentto work instakeholders small groups. Finwithinally, it theconduct stakeholders a of a node is proportional to its degree centrality Endowment Trust (Trust) have the highest [CD (n ) −CD (ni )] D ∑ degree indices. For a network with N nodes, the network.network Second,-level SNA it performto compares a thegroup stakeholder-level SNA to otherThewithin at least stakeholder the once network. per month. If networks a node In thishas figure,afor higher Indiana the degree size and OklahomaclosenessPartners centrality (areMHP shown) (0.39and andinTobacco Figure0.36, respectively)Settlement 7. A link in and i=1 C3 of acentrality node is thenproportional its size will to be its bigger degree and vicecentrality versa. IndianaEndowment and OklaTrusthoma (Trust) stakeholder have networks,the highest CD = degree………… centralisation (4) (i.e., C ) reaches its explorenetwork the of Indianatendency with ofthe stakeholderstakeholders’order networkto quantify preferences of the importance of different connects two stakeholders if they have contact with each other at least once per [(N −1)*(N − 2)] D withinThis the figurenetwork. therefore If a node gives has a higherquick degreevisual respectively.closeness centrality This indicates (0.39 andthat 0.36,they arerespectively) the most in maximum value of 1 when a node chooses all other Oklahoma. This article �irst conducts a node-level SNA in illustration about the connection(s) that each node reachable organisations from any other nodes to work in small groups. Finstakeholdersally, it conduct withins thea given stakeholder (N-1) nodes and the other (N-1) actors interact only Figure 5: A complete network where each node is connected centralityhas with then other its sizenetwork will benodes bigger within and the vice network. versa. withinIndiana theand Indiana Okla homaand Oklahoma stakeholder stakeholder networks, network-level SNA to comparenetwork. the Itstakeholder uses some SNA measures to the network. If a node has a higher degree centrality then its size will be bigger and with this actor (i.e., the situation in a star networkFIGURE 05. A completewith all networkother remaining where eachnodes node in the is network connected with all other remaining nodes in C3 ThisIn figurethe same therefore way, other givesnode- levela quickSNA measuresvisual networks,respectively. respectively. This indicates A thathigh they betweenness are the most Where, CnDi()are the degreeas inindices Figure of3). NThis nodes index attains its minimum network of Indiana with the stakeholder network of month. In this �igure, the size of a node is proportional to its degree centrality within the network 1 Center for Tobacco Policy Researchvisually (2005). Best distinguish the importance of dif-illustration(e.g., closeness about thecentrali connection(s)ty) can be used that toeach define node the centralityreachable (0.07)organisations for thefrom American any other Lung nodes * value of 0 when all degrees are equal (i.e., the The set of betweenness centralities (as in Oklahoma. size of a node within a network. Association (ALA) in the Oklahoma stakeholder practices project. Saint Louis University School of Public has with other network nodes within the network. within the Indiana and Oklahoma stakeholder and CD (n )is the largest observedsituation in avalue circle networkin the as in Figure 4). Thus, equation 3), which represents the collection of ferent stakeholders within the stakeholder tion(s)Table that1 shows each five node top stakeholders has with otherin respect network network nodes representswithin the that network.this organisation In the has same been a The set of betweennessbetweenness indices centralities of N nodes in(as a network,in equation can 3), which Health. http://escholarship.org/uc/item/6fs8f7p4 In thevice same versa. way, Thisother �igurenode-level therefore SNA measures gives a quicknetworks, visual illustrationrespectively. about A highthe connec-betweenness degree indices. For a networkCD withindicates N nodesthe ,varying the amount of the FIGURE 06. AIllustration of the community structure in an abstract network which has three network. Second, it performs a group-level to three basic centrality measures (i.e., degree, gatekeeper or controller of information flow centralisation of degree compared to both starrepresents and bethe summarised collection by of betweennessthe following equationindices toof N nodes in a communities (i.e., C1, C2 and C3) (e.g.closeness, closeness and centrali betweennessty) can be centrality) used to define in boththe betweencentrality any (0.07) pair offor other the nodes American within thLunge degree centralisation (i.e., ) reaches its measure the betweenness centralisation (L. 1 SNA toPage explore 5 of 9 the tendency of stakeholders’ thenetworks. size ofIndiana a node Tobaccowithin aPrevention network. and network. St. Joseph County (St. Joseph) plays a circleCD networks. network, can be summarised by the following equation to meas- Center for Tobacco Policy Research (2005). Best sizeway, of a node other within node-level a network. SNA measures (e.g., closenessAssociation centrality) (ALA) incan the be Oklahoma used to de�inestakeholder Freeman et al., 1979): preferences to work in small groups. Finally, Cessation Agency (ITPC) has the highest degree similar role within the Indiana stakeholder network. maximum value of 1 when a node chooses all other --- 3.3 COMMUNITY STRUCTURE --- practices project. Saint Louis University School of Public Tablecentrality 1 1shows within five the top stakeholderstakeholders network in respect of network represents that this organisation has been a ure the betweenness centralisation (L. Freeman et al., 1979): it conducts a network-level SNA to compare (N-1) nodes and the other (N-1) actors interact only N Figure 6: Illustration of the community structure in an abstract Health. http://escholarship.org/uc/item/6fs8f7p4 to threeIndiana. basic In fact,centrality it has measuresa degree centrality(i.e., degree, of 1, 4.2gatekeeper GROUP- LEVELor controller of information flow Figure 5: A completeN network where each node is connected Figure 6: Illustration of the community structure in an abstract (i.e., degree, closeness and betweenness centrality) in both networks. Indiana Tobac- ' * ' Page 4 of 9 A network is said to have a ‘community structure’ if the nodes of which indicated that ITPC has links with all other Figure 8 shows the community structure for both with this actor (i.e., the situation in a star network with all other remaining' nodes* in the' network network which has three communities (i.e., C1, C2 and C3) the stakeholder network of Indiana with the closeness and shows betweenness �ive top centrality) stakeholders in both in respectbetween to three any basicpair of centrality other nodes measures within the [C B (n ) −CB (ni )] network which has three communities (i.e., C1, C2 and C3) conodes Prevention and is at theand central Cessation position Agency within the(ITPC) hasIndiana the andhighest Oklahoma degree stakeholder centrality networks. within The ∑ [C B (n ) −CB (ni )] that network can easily be divided into sets of groups such that Page 5 of 9 networks. Indiana Tobacco Prevention and network. St. Joseph County (St. Joseph) plays a as in Figure 3). This index attains its minimum = ∑ stakeholder network of Oklahoma. network. This organisation therefore does not need algorithm proposed by Clauset et al. (2004) has i 1 = the stakeholder network of Indiana. In fact, it has a degree centrality of 1, which in- C B = i 1 …………. (6) Cessation Agency (ITPC) has the highest degree similar role within the Indiana stakeholder network. value of 0 when all degrees are equal (i.e., the TheC B =set of betweenness centralities………… (as. ( 6in) 3.3 3.3COMMUNITY COMMUNITYeach STRUCTURE set STRUCTUREof nodes is densely connected internally but sparsely to rely on other node(s) to establish a direct been used for this community structure analysis. (N −1()N −1) The required network analyses for this case dicatedcommunication that withITPC any has of thelinks remaining with nodesall other of nodesNodes and with is atsame the shape central and colourposition belong within to the situation in a circle network as in Figure 4). Thus, equation 3), which represents the collection of A networkA network is saidconnected is tosaid have to externally. havea ‘community a ‘community Each structure’set of structure’ nodes is called a ‘community’. centrality within the stakeholder network of betweennessWhere, Cindices(n ) are of the N nodesbetweenness in a network, indices can of N nodesif andthe Cnodes(n* of that network can easily be divided study have been conducted using two soft- Indiana.the network.In fact, it Thishas a organisationdegree centrality therefore of 1, does4.2 not GROUP need-LEVEL to rely on other node(s) to CD indicates the varying amount of the ' B i if theB nodes In theof that network network of Figurecan easily 6, there be divided are three communities (i.e., Page 6 of 9 Where,be summarised)Cn is ()the 'largestare theby observed betweennessthe following value indices in theequation betweenness of N to indices.into sets Free- of groups such that each set of nodes is whichestablish indicated a that direct ITPC communication has links with all otherwith any ofFigure the remaining 8 shows the nodes community of the structure network. for both centralisation of degree compared to both star and Where,Bi CnBi()are the betweenness indices of N into sets ofC1, groups C2 and such C3). thatAny nodeeach ofset these of nodes communities is has more links measure ' the* betweenness centralisation (L. densely connected internally but sparsely Analyzer (ORA) which was developed by the nodes and is at the central position within the Indiana and Oklahoma stakeholder networks. The circle networks. nodes andman (1978)' is the*demonstrates largest observed that betweennessvalue in centralisationdensely connected internally but sparsely Oklahoma State Department of Health Tobacco Use Prevention Service (TUPS) also nodes CandB ( nC )(n )is the largest observed value in connected externally.with other Each nodes set of of nodes the sameis called community a compared with the ware tools. The �irst one is Organizational Risk network. This organisation therefore does not need algorithm proposed by Clauset et al. (2004) has Freemanreaches et al., itsB 1979 maximum): value of 1 for the star graph. Itsconnected mini- externally. Each set of nodes is called a Center for Computational Analysis of Social has a degree centrality of close to 1 (i.e., 0.92) in the Oklahoma stakeholder network. the thebetweenness betweenness indices. indices. Freeman Freeman (1978 ()1978 ) ‘community’. Innumber the network of links of with Figure other 6, nodesthere arefrom other communities. This to rely on other node(s) to establish a direct been used for this community structure analysis. mum value of 0 occurs when all actors have exactly the‘community same ’. In the network of Figure 6, there are and Organizational System of the Carnegie communicationMadison Healthwith any Partnersof the remaining (MHP) nodes and of TobaccoNodes Settlement with same andshape Endowment and colour belong Trust to the demonstratesdemonstrates that thatbetweenness betweenness centralisation centralisation three communitiesmethod (i.e., is C1, used C2 to and conduct C3). Any a group-level node analysis of the under- reaches itsbetweenness maximum valueindex. of 1 for the star graph. three communities (i.e., C1, C2 and C3). Any node Mellon University (Carley, 2010). The second (Trust) have the highest closeness centrality (0.39 and 0.36, respectively) in Indiana reaches its maximum value of 1 for thePage star 4 graph.of 9 of theseof these communities communitieslying social has network. morehas more links linkswith withother other Its minimum value of 0 occurs when all actors have one is NodeXL which is a network analysis and and Oklahoma stakeholder networks, respectively. This indicates that they arePage the 6 of 9 Its minimum value of 0 occurs when all actors have nodesnodes of the of samethe same community community compared compared with withthe the exactly the--- same 3.2 NETWORK betweenness DENSITY index. --- visualisation software package for Microsoft most reachable organisations from any other nodes within the Indiana and Okla- exactly the same betweenness index. numbernumber of linksof linkswith withother other nodes nodes from fromother other 3.2 NETWORK DENSITY 4. STATE TOBACCO CONTROL PROJECTS IN THE UNITED Excel (Hansen, Shneiderman, & Smith, 2010). 3.2 NDensityETWORK is aDENSITY network-level SNA measure. The densitycommunities. of communities.a net- This Thismethod method is used is usedto conduct to conduct a a homa stakeholder networks, respectively. A high betweenness centrality (0.07) for DensityDensity workis a isrepresentsnetwork a network-level the- levelproportionSNA SNAmeasure. ofmeasure. existing The tiesThe (or, grouplinks)- levelrela- analysisSTATES of- A theCASE underlying STUDY OF social NETWORK ANALYSIS the American Lung Association (ALA) in the Oklahoma stakeholder network repre- density of a network represents the proportion of group-level analysis of the underlying social densitytive ofto thea network maximum represents number theof possibleproportion ties of among network all networknodes. . ------existing ties (or, links) relative to the maximum 1. Center for Tobacco Policy Research (2005). Best existingof that ties network (or, links) (S Wasserman relative to& Faust,the maximum 2003). The density value This case study has been considered from the article published practices project. Saint Louis University School between any pair of other nodes within the network. St. Joseph County (St. Joseph) numbernumber of possible of possible ties amongties among all nodes all nodes of that of that 4 STATE TOBACCO CONTROL PROJECTS IN THE of Public Health. http://escholarship.org/uc/ sents that this organisation has been a gatekeeper or controller of information �low for a network is 1 only when all nodes of that network are4 con- STATEby TOBACCO Crane (2007). CONTROL The network PROJECT analysisS IN THE data reported in this case item/6fs8f7p4 plays a similar role within the Indiana stakeholder network. networknetwork (S Wasserman (S Wasserman & Faust, & Faust, 2003 )2003. The). densityThe density UNITED STATES - A CASE STUDY OF NETWORK value for a network is 1 only when all nodes of that UNITED STATES - A CASE STUDY OF NETWORK value for a network is 1 only when all nodes of that ANALYSISANALYSIS networknetwork 110are connectedJOURNAL are connected OF MODERN with witheachPROJECT eachother MANAGEMENT other (i.e., (i.e.,in • MAY/AUGUSTthe in the • 2017This case study has been considered from the 2017 • JOURNALMODERNPM.COM 111 case of a complete network as in Figure 5). On the This case study has been considered from the case of a complete network as in Figure 5). On the articlearticle published published by Craneby Crane (2007 ()2007. The). Thenetwork network otherother hand, hand, for afor completely a completely sparse sparse network, network, the the analysis data reported in this case study came from density value is 0, which indicates there is no link analysis data reported in this case study came from density value is 0, which indicates there is no link two twolarge -largescale- scalemultistate multistate projects projects to evaluateto evaluate existsexists between between any twoany nodestwo nodes of that of network.that network. For For tobacco control programs. These projects were an undirected network of size N, theoretically there tobacco control programs. These projects were an undirected network of size N, theoretically there conductedconducted by theby Centrethe Centre for Tobaccofor Tobacco Policy Policy are (i.e., N )N possible links Research of the Saint Louis University School of [areN *[(NN*−(1N)]−/ 21)]/ 2 (i.e.C2, C ) possible links Research of the Saint Louis University School of 2 Public Health and had been funded by the among its N nodes. If there are N links among its Public Health and had been funded by the among its N nodes. If there aret Nt links among its American Legacy Foundation and the Chronic American Legacy Foundation1 and the Chronic N nodes in that network, then, mathematically, 1 N nodes in that network, then, mathematically, DiseaseDisease Directors Directors Association Association. The. networkThe network data isdata is density can be defined as (S Wasserman & Faust, density can be defined as (S Wasserman & Faust, aboutabout the theconnectivity connectivity among among different different 2003): 2003): stakeholdersstakeholders in two in differenttwo different states states (Indiana (Indiana and and 2× N Oklahoma). A connection between stakeholders is 2t × N……………….t (7) Oklahoma). A connection between stakeholders is DensityDensity= = ………………. (7) broadly defined and includes face-to-face meeting, NN×−(NN×− 1)( 1) broadly defined and includes face-to-face meeting, telephonetelephone conversations conversations and emails.and emails. This Tnetworkhis network data datawas wascollected collected by bysurveying surveying different different The densityThe density of the of network the network as in asFigure in Figure 2 is 0.52 is 0.5 stakeholdersstakeholders in these in these two statestwo states in 2002 in .2002 Each. Eachof of (i.e., (i.e.,(2×5)/(5 (2××5)/(54) =× 4)0.5) = since0.5) since it has it 5 has links 5 linksamong among thesethese states states was wasrated ratedagainst against some some criteria criteria for for its fiveits nodesfive nodes and thereand therecan becan maximum be maximum 10 links 10 links financialfinancial and politicaland political climate. climate. According According to this to this amongamong these these 5 nodes. 5 nodes. Density Density describes describes the general the general rating,rating, which which was conductedwas conducted in 2002, in 2002, Indiana Indiana was was level levelof cohesionof cohesion in ain network;a network; whereas, whereas, foundfound ‘strong’ ‘strong’ for havingfor having both bothpositive positive financial financial centralisationcentralisation describes describes the extentthe extent to which to which this this and andpolitical political climates; climates; whereas, whereas, Oklahoma Oklahoma was was cohesioncohesion is organisedis organised around around particular particular focal focal indexedindexed as ‘weak’as ‘weak’ against against these these two twoclimate climate nodes.nodes. Centralisation Centralisation and anddensity, density, therefore, therefore, are are conditionsconditions (Crane, (Crane, 2007 )2007. This). Thisarticle article first conductfirst conducts s importantimportant complementary complementary measures. measures. a nodea -nodelevel- levelSNA SNAin orderin order to quantifyto quantify the the

importanceimportance of differentof different stakeholders stakeholders within within the the C1 C1 C2 C2 givengiven stakeholder stakeholder network. network. It use Its usesomes some SNA SNA measuresmeasures to visually to visually distinguish distinguish the importance the importance of of

differentdifferent stakeholders stakeholders within within the thestakeholder stakeholder network.network. Second, Second, it perform it performs a groups a group-level- levelSNA SNAto to explore the tendency of stakeholders’ preferences explore the tendency of stakeholders’ preferences to workto work in small in small groups. groups. Finally, Fin ally,it conduct it conducts a s a network-level SNA to compare the stakeholder C3 network-level SNA to compare the stakeholder C3 networknetwork of Indiana of Indiana with withthe stakeholder the stakeholder network network of of Oklahoma. Oklahoma.

1 Center1 Center for Tobacco for Tobacco Policy Policy Research Research (2005) (2005). Best. Best practices project. Saint Louis University School of Public practices project. Saint Louis University School of Public Health.Health. http://escholarship.o http://escholarship.org/uc/item/6fs8f7p4rg/uc/item/6fs8f7p4

Page 5Page of 9 5 of 9

same community in both stakeholder networks. members. Oklahoma network has also two There are two communities found in the Indiana communities with seven and six members, network. As in Figure 8(a), the first community respectively (Figure 8(b)). (represented by black solid circle) has nine members; whereas, the second community (represented by green solid triangle) has six

SOCIAL NETWORK ANALYSIS IN PROJECT MANAGEMENT - A CASE STUDY OF ANALYSING STAKEHOLDER NETWORKS (a) Indiana (b) Oklahoma

Figure 8: Community structure analysis of Indiana and Oklahoma stakeholder networks. Nodes having same colour and shape belong to the same community in both networks. The size of a node in both networks is proportional to its degree centrality value. ods in the context of project management, nity structure analysis) in exploring two stakeholder networks. lation among stakeholders on the development of other type --- 4.2 GROUP-LEVEL --- particularly for analysing two stakeholder Some other advanced level SNA methods can also be used in of relation among the same group of stakeholders. Application Figure 8 shows4. the3 N communityETWORK-LEVEL structure for both Indiana and Oklahoma stakehold-This article provides an illustration about the Based on different network-level SNA measures, a applicationnetworks. of SNA It also measures shows how and two methods different in the the context of project management. For example, the network of such advanced level network methods could be the research er networks. The algorithm proposed by Clauset et al. (2004) has been used for this comparison between the stakeholder networks of contextstakeholder of project networks management that may,, particularly or may not, for regression can be used to explore the impact of one type of re- topic of any future project management research. community structure analysis. Nodes with same shape and colour belong to the Indiana and Oklahoma has been presented in Table analysinghave two same stakeholder member nodes networks. and links It amongalso shows same community in both stakeholder networks. There are two communities found 2. As presented in this table, the stakeholder how twothem different can be comparedstakeholder using networks various thatSNA may, samein the community Indiana network.in both stakeholder As in Figure networks. 8(a) members. Oklahoma network has also two There are two communitiesnetwork found of Indiana in the Indiana has highercommunities degree and with closeness seven and six members,or may measures not, have and samemethods. member This type nodes of network and links • LIST OF ABBREVIATIONS • solid circle) has nine members; whereas, the second community (represented by network. As in Figurecentralisatio 8(a), the firstn values community compared , the �irstrespectively with community the (Figure stakeholder 8(b)).(represented by blackamong analysisthem can can be be ofcompared help to project using managersvarious SNA (representedgreen solid by triangle) black solid has sixcircle) members. has nine Oklahoma network has also two communities network of Oklahoma. The stakeholder network of measuresor otherand relevantmethods. decision This makers. type Theyof can,network members;with seven whereas, and six the members, second respectivelycommunity ( ). (represented by greenOklahoma solid triangle) has hasslightly six Figure higher 8(b) betweenness analysis can be of help to project managers or other ACS → American Cancer Society Latino → Latino Agency St. Joseph → St. Joseph County AHA → American Heart Association Latino Inst → Indiana Latino Institute SW Coalition → Southwest Tobacco Free Oklahoma Coalition centralisation (0.06 versus 004) and network relevantplaying decision the central makers. role withinThey thecan, stakeholder for example, ALA → American Lung Association MHP → Madison Health Partners for example, �igure out which stakeholder is Alliance → Oklahoma Alliance on Health or Tobacco MZD → MZD Advertising TFK → Tobacco Free Kids density values (0.30 versus 0.29) compared with figure outnetwork which and stakeholder allocate the availableis playing resources the central Shahadat Uddin [email protected] B&GDr Shahadat Uddin of IN → Indiana is a lecturer in the Project Management Program & Alliance of Boys and Girls Clubs Complex Systems Research NE Coalition → Northeast Tobacco Free Oklahoma Coalition Trust → Tobacco Settlement Endowment Trust the Indiana stakeholder network. Therefore, the role withinaccordingly the stakeholder for the successful network completion and allocate of the BartholomewCentre at the University of Sydney. He conducts research in the area of complex (longitudinal) networks, → Bartholomew County OICA → Oklahoma Institute for Child Advocacy TulsaHD → Tulsa City-County Health Department DOHdata analytics and modelling. His research addresses interdisciplinary issues related to understanding → Indiana State Department of Health OSMA → Oklahoma State Medical Association Use Prevention Service stakeholder network of Indiana has a higher level available resources accordingly for the successful the impact of network structure and dynamics on group performance and coordination outcomes in TUPS → Oklahoma State Department of Health Tobacco the underlying project. Further, by conduct- ITPCcomplex, dynamic and distributed environments. As application areas, he has been exploring these → Indiana Tobacco Prevention and Cessation PWorkz → PreventionWorkz cohesive network structure compared with the completion of the underlying project. Further, by ITPCresearch challenges in the context of healthcare coordination, scientific workforce an Board → Indiana Tobacco Prevention and Cessation Board d project SF IN → Smoke Free Indiana ing the similar network analysis of the same management. Dr Uddin has published in several international journals including Scientific Reports, stakeholder network of Oklahoma. Since Indiana conducting the similar network analysis of the IUComplexity and Journal of Informetrics. He was awarded the Dean’s Research Award 2014 by the School of Med → Indiana University School of Medicine SFMC → Smoke Free Marion County UofO → University of Oklahoma Health Sciences Center stakeholder network over the time, they can University of Sydney in recognition of his outstanding research achievement as an early career and Oklahoma had been indexed as ‘strong’ and same stakeholder network over the time, they can researcher. monitor the ongoing progress of the project. • AUTHOR • ‘weak’ for the political and financial climates, monitor the ongoing progress of the project. in complex, dynamic and distributed environments. As application areas, he has been Any node-level SNA approach usually fo- DR SHAHADAT UDDIN is a lecturer in the Project Management Program respectively when their network datasets were Any node-level SNA approach usually focuses & Complex Systems Research Centre at the University of Sydney. He collected, it can be argued that superior network on questionscuses on, suchquestions, as, “Wsuchhich as, “Whichorganisations organ- are conducts research in the area of complex (longitudinal) networks, workforce and project management. Dr Uddin has published in several international data analytics and modelling. His research addresses interdisciplinary exploring these research challenges in the context of healthcare coordination, scienti�ic cohesiveness is positively associated with strong most centralisations inare the most network? central in”; the“Are network?”; the central issues related to understanding the impact of network structure awarded the Dean’s Research Award 2014 by the University of Sydney in recognition of his political and financial climate. organisation“Are the(s) essentialcentral organisation(s) for addressing essential the needs of and dynamics on group performance and coordination outcomes outstandingjournals including research Scienti�ic achievement Reports, as an Complexity early career and researcher. Journal of Informetrics. He was (a) Indiana (b) Oklahoma a project for its successful completion?”; “Does Figure 8: Community structure analysis of Indiana and Oklahoma stakeholder networks. Nodes having same colour and shape belong to the for addressing the needs of a project for its FIGURE 08. Community structure analysis of Indiana and Oklahoma stakeholder networks. Nodes having same colour and shape belong to the same community in bothTable networks. 2: The Values size of a nodeof in differentboth networks network is proportional-level to its degreesocial centrality network value. same community in both networks. The size of a node in both networks is proportional to its degree centrality value. the networksuccessful has completion?”;any connector, “Does information the network broker analysis measures for Indiana and Oklahoma stakeholder and boundary spanner?”; and “If the answer of the 4.3 NETWORK-LEVELnetworks. This article provides an illustration about the has any connector, information broker and Based on different network-level SNA measures, a application of SNA measures and methods in the • REFERENCES • Network-level measure Indiana Oklahoma previousboundary question spanner?”; is ‘yes’ and “Ifthen the answerwho are of the comparison between the stakeholder networks of context of project management, particularly for Berkowitz, S. (1982). An introduction to structural anal- matical Organization Theory, 11(3), 201-228. ing key challenges in major public engineering projects by Indiana and Oklahoma1. hasNetwork been presented centralisation in Table analysing two stakeholder networks. It alsoconnector(s), shows information broker(s) and boundary the previous question is ‘yes’ then who are ysis: The network approach to social research: Butter- Freeman, L. (1978). Centrality in social networks: Concep- a network-theory based analysis of stakeholder concerns: 2. As presented in this Degreetable, thecentralisation stakeholder how two0.24 different stakeholder0.19 networks thatspanner(s) may, in the network?”. The principal focus of worth-Heinemann. A case study. International Journal of Project Management, the connector(s), information broker(s) network of Indiana has higherCloseness degree and centralisation closeness or may0.54 not, have same0.46 member nodes and links 35(1), 78-94. a group-level SNA approach is to group a set of Freeman, L. (2004). The development of social network centralisation values compared with the stakeholder among them can be compared using various SNA and boundary spanner(s) in the network?”. works, 27(1), 55-71. tual clari�ication. Social Networks, 1(3), 215-239. Betweenness centralisation 0.04 0.06 nodes based on the similarity of their structural analysis: Empirical Press Vancouver, British Columbia. Mullins, N., & Mullins, C. (1973). Theories and theory groups network of Oklahoma. The stakeholder network of measures and methods. This type of network Borgatti, S.S. (2005). P., Everett, Centrality M. G., and & networkFreeman, �low. L. SocialC. (2002). Net- in contemporary American sociology: Harper & Row. 2. Network density 0.29 0.30 The principal focus of a group-level SNA ap- Freeman, L., Roeder, D., & Mulholland, R. (1979). Centrality Oklahoma has slightly higher betweenness analysis can be of help to project managers orpositions other within the network. Therefore, the focus UCINET for Windows: Software for social network analysis. Nadel, S. (1957). The theory of social structure (London, Co- centralisationTABLE 02. LValues(0.06 of versusdiff erent network-level004) and socialnetwork network analysis measuresrelevant for decisionIndiana and makers.Oklahoma stakeholderThey can, networks. for example, proach is to group a set of nodes based on in Social Networks: II. Experimental Results. Social Net- of any group-level SNA approach on questions, as Brandes, U., & Fleischer, D. (2005). Centrality measures works, 2(80), 119-141. hen & West): Ltd. density values (0.30 versus 0.29) compared with figure out which stakeholder is playing the central the similarity of their structural positions the Indiana stakeholder network. Therefore, the role within the stakeholder network and allocate the Freeman, L. C., White, D. R., & Romney, A. K. (1992). Research Newig, J., Günther, D., & Pahl-Wostl, C. (2010). Synapses in the --- 4.3 NETWORK-LEVEL --- like, “Is the network divided into subgroups or network: learning in governance networks in the context of stakeholder network5 of D IndianaISCUSSION has a higher AND level CONCLUSION available resources accordingly for the successful within the network. Therefore, the focus of Carley, K. (2010). Center for Computational Analysis of So- methods in social network analysis: Transaction Publishers. cliques?” or “Are there any tendency of actors to cialbased and on Organizational current �low. Systems (CASOS), Institute for Soft- environmental management. Ecology and Society, 15(4), 24. cohesiveBased onnetwork different structure network-level compared with SNA the measures, completion a comparison of the underlying between project. the Further, stake- by any group-level SNA approach on questions, ware Research International (ISRI). School of Computer Pich, M. T., Loch, C. H., & Meyer, A. D. (2002). On uncertainty, stakeholder network of Oklahoma. Since Indiana conducting the similar network analysis workof the into groups?”. The key consideration of the Science, Carnegie Mellon University, 5000 Forbes Avenue weak ties in intraorganizational social networks. Social andholder Oklahoma networks had been of indexedIndiana as and‘strong’ Oklahoma and hassame been stakeholder presented network in overTable the 2time,. As theypre- can as like, “Is the network divided into sub- Networks,Friedkin, N. 3(4), (1982). 273-285. Information �low through strong and ambiguity, and complexity in project management. Manage- Pittsburgh, PA 15213-3890. ment science, 48(8), 1008-1023. ‘weak’sented for in thethis political table, theand stakeholderfinancial climates network, ofmonitor Indiana the ongoinghas higher progress degree of the andproject. close- Gluckman, M. (1973). The judicial process among the Barot- groups or cliques?” or “Are there any ten- Carlsson, L., & Sandström, A. (2008). Network governance Prell, C., Hubacek, K., & Reed, M. (2009). Stakeholder analysis respectively when their network datasets were Any node-level SNA approach usually focuses Page 7 of 9 of the commons. International Journal of the Commons, se of Northern Rhodesia (Zambia): Humanities Press Intl. ness centralisation values compared with the stakeholder network of Oklahoma. The and social network analysis in natural resource manage- collected, it can be argued that superior network on questions, such as, “Which organisations are dency of actors to work into groups?”. The 2(1), 33-54. Hagedoorn, J. (1996). Trends and patterns in strategic cohesiveness is positively associated with strong most central in the network?”; “Are the central ment. Society and Natural Resources, 22(6), 501-518. stakeholder network of Oklahoma has slightly higher betweenness centralisation key consideration of the network-level SNA Carrington, P., Scott, J., & Wasserman, S. (2005). Models and technology partnering since the early seventies. Review of Pryke, S. D. (2004). Analysing construction project coali- political and financial climate. organisation(s) essential for addressing the needs of methods in social network analysis. New York: Cambridge industrial Organization, 11(5), 601-616. (0.06 versus 004) and network density values a(0.30 project versus for its 0.29) successful compared completion? with”; the“Does approach is to explore the cohesiveness of tions: exploring the application of social network analysis. University Press. Hansen, D., Shneiderman, B., & Smith, M. A. (2010). Ana- Table 2: Values of different network-level social network the network has any connector, information broker Construction Management and Economics, 22(8), 787-797. Indiana stakeholder network. Therefore, the stakeholder network of Indiana has a the entire network. This cohesiveness can Chinowsky, P. S., Diekmann, J., & O’Brien, J. (2009). Project lyzing social media networks with NodeXL: Insights from analysis measures for Indiana and Oklahoma stakeholder and boundary spanner?”; and “If the answer of the Scott, J. (1988). Social network analysis. Sociology, 22(1), networks.higher level cohesive network structure compared with the stakeholder network of organizations as social networks. Journal of Construction a connected world: Morgan Kaufmann. Network-level measure Indiana Oklahoma previous question is ‘yes’ then who are the also be used to compare multiple different Engineering and Management, 136(4), 452-458. 109-127. connector(s), information broker(s) and boundary Hummon, N. P., & Carley, K. (1993). Social networks as nor- Oklahoma.1. Network centralisation Since Indiana and Oklahoma had been indexed as ‘strong’ and ‘weak’ for networks and to answer questions, such as, Clauset, A., Newman, M. E., & Moore, C. (2004). Finding com- Tichy, N. M., Tushman, M. L., & Fombrun, C. (1979). Social Degree centralisation 0.24 0.19 spanner(s) in the network?”. The principal focus of munity structure in very large networks. Physical Review E, network analysis for organizations. Academy of Manage- Closeness centralisation 0.54 0.46 “How overall sustainability of the network Leinhardt, G. (1977). Program evaluation: An empirical a group-level SNA approach is to group a set of 70(6), 066111. mal science∗. Social Networks, 15(1), 71-106. ment Review, 4(4), 507-519. Betweenness centralisation 0.04 0.06 nodes based on the similarity of their structural study of individualized instruction. American Educational collected,2. Network density it can be argued0.29 that superior0.30 network cohesiveness is positively associat- can be enhanced?” or “How the multi-organ- Uddin, S. (2016). Exploring the impact of different multi-lev- positions within the network. Therefore, the focus Crane, D. (2007). Understanding and managing stakeholder Research Journal, 14(3), 277-293. the political and �inancial climates, respectively when their network datasets were networks. Greater than the sum: systems thinking in tobacco el measures of physician communities in patient-centric care of any group-level SNA approach on questions, as isational services provided to a client group Marsden, P. V., & Lin, N. (1982). Social structure and net- control. Washington (DC): National Cancer Institute, 147-183. networks on healthcare outcomes: A multi-level regression like, “Is the network divided into subgroups or work analysis: Sage Beverly Hills. 5 DISCUSSION AND CONCLUSION might be strengthened?”. De Nooy, W., Mrvar, A., & Batagelj, V. (2011). Exploratory cliques?” or “Are there any tendency of actors to Mitchell, J. (1966). Theoretical orientations in African urban ed with strong political and �inancial climate. social network analysis with Pajek (Vol. 27): Cambridge Wasserman, S., & Faust, K. (2003). Social network anal- work into groups?”. The key consideration of the studies. The social anthropology of complex societies, 37-68. approach. Scienti�ic reports, 6, 20222. 5. DISCUSSION AND CONCLUSION This article uses few basic level SNA meas- University Press. ysis: Methods and applications. Cambridge: Cambridge Mitchell, J. (1969). The concept and use of social networks. University Press. ------ures (i.e., centrality, centralisation and net- Diesner, J., Frantz, T., & Carley, K. (2005). Communication Page 7 of 9 Networks from the Enron Email Corpus “It's Always About Social networks in urban situations, 1-50. Wasserman, S., & Iacobucci, D. (1988). Sequential social net- This article provides an illustration about the application of SNA measures and meth- work density) and methods (i.e., commu- the People. Enron is no Different”. Computational & Mathe- Mok, K. Y., Shen, G. Q., Yang, R. J., & Li, C. Z. (2017). Investigat- work data. Psychometrika, 53(2), 261-282.

112 JOURNAL OF MODERN PROJECT MANAGEMENT • MAY/AUGUST • 2017 2017 • JOURNALMODERNPM.COM 113