Evaluating Twitter Influence Ranking with System Theory
Georgios Drakopoulos, Andreas Kanavos and Athanasios Tsakalidis Computer Engineering and Informatics Department, University of Patras, Patras 26500, Greece
Keywords: Functional Metrics, Structural Metrics, Graph Databases, Higher Order Data, Influence Ranking, Neo4j.
Abstract: A considerable part of social network analysis literature is dedicated to determining which individuals are to be considered as influential in particular social settings. Most established algorithms, such as Freeman and Katz- Bonacich centrality metrics, place emphasis on various structural properties of the social graph. Although this makes centrality metrics generic enough to be applied in virtually any setting, they are oblivious to the functionality of the underlying social network. This paper examines five social influence metrics designed especially for Twitter and their implementation in a Java client retrieving network information from a Neo4j server. Additionally, a sceheme is proposed for evaluating the performance of an influence ranking based on estimating the exponent of a Zipf model fitted to the ranking score.
1 INTRODUCTION processing systems such as Spark (Robinson et al., 2013)(Onofrio Panzarino, 2014). Social media constitute a mainstay of the connected The primary contribution of this work is three- age. Recently, Twitter has emerged among them as fold. Five Tweeter-specific metrics capturing essen- one of the most popular microblogging platforms, tial online behavior characteristics have been devel- where on a daily basis a vast amount of information, oped. Additionally, a methodology for evaluating in- including tweets and hashtags, is posted by the users fluence metrics based on concepts from system the- of the platform to the public or to selected circles of ory is proposed. Finally, the aforementioned metrics their contacts. have been implemented in Java over Neo4j through Their advent made feasible the application of the Cypher API. both traditional and innovative social network anal- The rest of this paper is structured as follows. Sec- ysis methods in previously prohibitive magnitude tion 2 summarizes the influence ranking literature. for cornerstone problems such as social coher- Implementation aspects are described in section 3. ence, social graph clustering, expansion potential, Twitter-specific functional metrics are outlined in sec- or information flow (Russell, 2013)(Leskovec et al., tion 4. Section 5 discusses the experimental results 2014)(Leskovec, 2011). Currently, social influence and the metric evaluation methodology, while section ranking has been recognized as an important research 6 explores future research directions. topic. Existing influence metrics rely heavily on structural properties of the social graph, such as the Table 1: Symbols used in this paper. number of shortest paths through a given vertex. Al- Symbol Meaning though these structural metrics are well defined and =4 Equality by definition can be applied to literally every social graph, they ig- x ,...,x Set containing elements x ,...,x nore the array of functions each social network per- 1 n 1 n {S } Cardinality of set S forms. | | τS ,S Tanimoto coefficient of sets S and S Graph databases such as Neo4j provide produc- 1 2 1 2 tk k-th Twitter user (used as shorthand) tion grade front- or back-end social graph storage. µ Twitter user influence metric Moreover, they offer graph analytics such as link µk Influence score of tk assigned by µ prediction, shortest paths, clustering coefficient, and µ1 µ2 Metric µ1 outperforms µ2 minimum spanning trees, bolstering the potential µ1 µ2 Metric µ1 is at least as good as µ2 of graph tools such as NetworkX, machine learn- ing frameworks such as Graphlab, and distribiuted
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Drakopoulos, G., Kanavos, A. and Tsakalidis, A. Evaluating Twitter Influence Ranking with System Theory. In Proceedings of the 12th International Conference on Web Information Systems and Technologies (WEBIST 2016) - Volume 1, pages 113-120 ISBN: 978-989-758-186-1 Copyright c 2016 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
WEBIST 2016 - 12th International Conference on Web Information Systems and Technologies
2 RELATED WORK 3 SYSTEM ARCHITECTURE
Social network analysis scientific literature abounds Figure 1 illustrates the components of the system de- with influence rankings or metrics (Kempe et al., veloped to address the needs of this work as well as 2003). Although ranking classification is not always the information flow between them. The three main clear, distinct metric design methodologies can be functions are to retrieve the social graph through the broadly classified to structural and functional, while social media crawler, to store it in the Neo4j server, the former can be further subdivided to combinato- and to query this graph through its Java client. rial and spectral. Structural metrics are more versatile than functional ones, since the former are network- independent. On the contrary, the latter are network- specific but they tend to reveal more information about the underlying network. Combinatorial rankings compute the influence score based on basic graph properties. Prominent metrics of this category are the degree metric, namely the neighborhood size of a given vertex, and the Newman-Girvan centrality, a function of the graph shortest paths (Leskovec et al., 2014). Combinato- rial rankings may as well be expressed in the linear Figure 1: System architecture. algebra domain through the graph adjacency matrix. One such example is the Katz centrality (Katz, 1953). The social crawler, described in (Kafeza et al., Spectral rankings derive the influence score di- 2014), has been programmed in Twitter4j to collect rectly or indirectly through the spectral decomposi- im JSON format data such as tweets, retweets, and tion of the graph adjacency matrix. Eigenvalues and hashtags. It communicates with the Neo4j server eigenvectors play an important role in metrics such as through the Cypher API, a Java interface extended by PageRank (Leskovec et al., 2014) or eigenvector cen- Neo4j to Java clients, in order to populate the graph trality (Drakopoulos et al., 2015). database. The crawler is inaccessible from the client. On the contrary, functional metrics are associ- The Neo4j version is 2.2.5, the latest available version ated with particular aspects of a given social net- at the beginning of system development. It commu- work performs. TwitterRank (Weng et al., 2010) and nicates both with the Twitter crawler and the client. TunkRank (TunkRank, 2015) are two PageRank ex- The expressive power of Cypher, its declarative query tensions which take into account user similarity and language, reduces relatively complex graph queries to retweet probability respectively. In (Bakshy et al., simple patterns modifiable dynamically by the Java 2011) the most influential users are also the most cost- client. Since only the API is visible by the client, it is effective ones, where the cost is defined in terms of listed as a grey box, while the graph database proper overall communication complexity. In (Mehta et al., as a black box. On the end user side, the client has 2012) influence is expressed in terms of a sophisti- been developed in Java using the libraries available in cated metric incorporating structural and functional NetBeans for interfacing with Neo4j. elements. In (Pal and Counts, 2011) the problem of The need for new database approaches, besides finding the most influential authors for a given topic in the relational one, was highlighted with the advent Twitter are selected from a Gaussian Mixture Model. of Web 2.0, which is dominated by high velocity, A similar problem in Yahoo! Answers was addressed unstructured or semistructured and high order data. in (Bouguessa et al., 2008), where ranking is done as Neo4j, a NoSQL graph database, stores data physi- a mixture of gamma distributions. cally as a graph. Finally, authors in (Rogers and Beal, 1957) move Property 1. Neo4j is schemaless (Robinson et al., along a different reasoning beyond the structural and 2013). functional divisive line, presenting influence in terms This is a fundamental NoSQL characteristic which of an intuition stemming from the current technolog- yields design flexibility but also imposes additional ical evolution, which eventually led to the successful design and administration burdens. spread of online social media. Quoting (Cha et al., 2010), influence is Property 2. The relational ACID operational re- quirements have been replaced by the three BASE “[. . . ] the ability of a person to influence the requirements (Robinson et al., 2013)(Onofrio Pan- thoughts or actions of others.” zarino, 2014).
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The BASE set is less strict than the ACID ’followers’: x, one, providing implementation flexibility and ease of ’frequency’: x, maintenance at the expense of data consistency. De- ’hashtags’: x ) spite the latter, a NoSQL database can be in practice } successfully tailored to the local operational demands. where x denotes a value computed elsewhere in the source code. The above Cypher command creates a Property 3. The property graph model is the primary vertex n of type user along with a set of associated conceptual data model supported by Neo4j and of- key-value pairs. This makes the conceptual graph ho- fered to a high level user typically through the Cypher mogeneous in the sense that each vertex has the same querying language (Drakopoulos et al., 2015)(Kon- number of key-value pairs. Moreover, there are no topoulos and Drakopoulos, 2014). missing values. Therefore, an implicit schema does Property 4. Neo4j fully supports for both vertices exist for the vertices of the particular Twitter graph, and edges the CRUD set of operations, namely but this need not to be the case generally. Create, Read, Update, and Delete. In a similar manner, if a user u follows another Neo4j supports Cypher, a declarative, ASCII art, user v, then an edge with the FOLLOWS tag (and and pattern based query language for handling con- FOLLOWEDBY) is created: ceptual graphs. Cypher possesses suitable syntax to c r e a t e ( ( u ) [:FOLLOWS] >(v ) , concisely express CRUD operations. For instance, a ( v ) −[:FOLLOWEDBY]− >(u ) ) vertex can be inserted with the command − − Notice that the inverse relationship has also been es- c r e a t e
tablished in a similar manner. Although this is by Similarly, a vertex can be removed with the com- no means necessary, finding the number of Followers mand that a given user has, facilitates subsequent analysis. Based on the above attributes, a range of cate- d e l e t e
gories for influential Twitter users can be constructed Deleting a vertex leads to the deletion of all of its in- depending on their online activity as in (Kafeza et al., and out-bound edges. 2013). The basic structure of a Cypher query is: Atomic conversational users have a high number match
of tweets and retweets. The rationale is that active [ with [< p a t t e r n >]] users either generate or relay a significant amount where [< constraints >] of information and they are therefore consulted by a return
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match ( n : u s e r ) l i m i t x n with I order by n . h a s h t a g s desc Atomic influential users, denoted by µ , combine l i m i t x in a sense the above notions as their overall influence s e t n:multisystemic score Ik is computed as in (Kafeza et al., 2013):
Subsequently, the users marked as multisystemic are I 4 µk = Tk Rk Ck log10 (1 + Fk)Qk Hk (1) returned along with the number of corresponding hashtags. The number of followers Fk is in base 10 logarithm for avoiding outliers. In addition, Fk is incremented by 1 match (n:multisystemic) so as to avoid a minus infinity metric when a user has return n , id (n), n.hastags as h no followers. The following Cypher command returns order by h desc these statistics for a given user Atomic energetic users, denoted by µ , have a E ( n : u s e r ) high number of Tweets over a specified time interval. match n This behavior pattern likely indicates a user knowl- with n, n.tweets , n.retweets , edgeable of or at least one strongly opinionated about return n . h a s h t a g s a particular topic. Thus, users curious to know about this topic or, correspondingly, like minded users may Also, the number of followers has been computed choose to consider this user an authority. for each user. For each user its score was computed match ( n : u s e r ) according to (1) and was stored as a new property return n , n . t w e e t s named overall to the appropriate vertex. Having order by n . t w e e t s desc computed this property, the following command re- turns the top influential users according to (1) and Notice that the above command retrieves the users changes their type to influential: sorted in descending order according to the total num- ber of their Tweets as well as their corresponding match ( n : u s e r ) number of Tweets they have posted. The time each with n Tweet was posted as well as the time resolution de- order by n . o v e r a l l desc termining which user is atomic energetic takes place l i m i t x elsewhere in the source code. The actual time reso- s e t n:influential lution was three days, which is a reasonably enough time to post a tweet, read a reply, and in following to post a new tweet. Atomic popular users, denoted by µP, have a high 5 RESULTS number of followers. Although popularity, in Twit- ter terms, does not necessarily translate to actual po- 5.1 Twitter Subgraph Synopsis pularity, highly followed users can be expected to at least be read by other Twitter users, exerting thus an A Twitter egg is an account with no fol- at least limited amount of influence. The number of Definition 1. lowers. users who connect to a given user through an edge can be identified by Definition 2. A star is a bipartite graph where the one parition is a singleton. Moreover, the vertex of ( n : u s e r ’ name ’ : x ) match this singleton is connected to all remaining vertices. < [:FOLLOWS]{ (u ) } − − return n , count ( d i s t i n c t u ) The Twitter subgraph was collected in a time inter- as f o l l o w e r s val of two months (September and October of 2015). order by f o l l o w e r s desc Its properties are stated in table 2. The first column l i m i t x has fundamental graph structure properties such as the number of edges and triangles, whereas the sec- or by the quicker query ond column has Twitter specific properties such as the match ( n : u s e r average tweet length and the average number of fol- ’ name ’ : x [:FOLLOWEDBY] >(u ) ) lowers. Note that the vertices are accounts and the { } − − return n , count ( d i s t i n c t u ) directed edges represent “following” relationships. as f o l l o w e r s There is only a small fraction of eggs and stars. order by f o l l o w e r s desc Specifically, there are 31 stars are comprised of 148
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Table 2: Twitter subgraph properties. alistic subgraph, the selection of a single topic facili- Property Value Property Value tates the analysis. Vertices 6561 Hashtags 417 In order to gain a deeper insight of the behavior Edges 35422 Tweets 18221 of Twitter analytics, the ranking scores are shown in Triangles 213 Retweets 7221 figures 2, 3, and 4. Initially there are more tweets Squares 72 Avg.following 2.11 than retweets, but eventually retweets rise to an al- Stars 31 Avg. followers 4.61 most steady fraction of tweets. Also, there are iner- Components 32 Eggs 117 leaving periods where retweets are anticorrelated with Diameter 9 Avg. tweet 102.8 tweets and periods where retweets are correlated with twewets. Table 3: Influential Twitter subgraph accounts breakdown. Concerning figure 3, conversational ranking scree values are a bit higher than the influential ones, Account type Instances though they both tend to have percentages equal to Official university account 1 1% after rank 60. For the conversational ranking scree Official school accounts 8 plot, the two major percentage decreases take place Official department accounts 22 for rank ranges starting from 5 to 35 and from 45 un- Faculty member accounts 46 til 65. For the influential ranking scree plot, there Student leader accounts 23 are also two decreases but smoother than in conver- Organization accounts 20 sational one; the first starts from rank equal to 1 until Total 120 5 and the second from 10 to 50. On the other hand, regarding figure 4, user rank- vertices, namely the 117 eggs plus the 31 central ver- ing logscree plots, for both conversational and influ- tices. By the very definition of the egonet, its diam- ential scores, seem to have almost the same behavior. eter equals 2. The remaining 6413 vertices belong to More concretely, conversational values are bigger un- a single, large component which is densely connected til rank 60, while influential values are by little bigger since its diameter equals 9. These structural charac- for the next 10 ranks. Then all the remaining ranks teristics indicate an active social network. have percentages equal to 1%. This is corroborated in the functional level by the A secondary finding is that accounts who reg- large number of hashtags, indicative of topic varia- ularly tweet usually have more influence than ones tions, and by the numerous and lengthy tweets. The who mostly retweet, although there are many excep- daily tweet and retweet traffic as shown in figure 2 tions to that rule. This is expected as accounts who has variations and bursts, signifying an active online post new tweets can be considered as potential influ- community. Notice that in figure 2 the tweets and the encers. Also, retweeting typically adds more status to retweets are expressed as percentages of the raw total the poster of the original tweet than to its retransmit- number of tweets and retweets respectively. ter. The exception to the rule seems to be users who The Tweeter crawler began its search from the of- selectively retweet about specific topics, acting in this ficial account of a prominent university and it was way as information hubs for these particular topics. programmed to contain its search strictly within ed- ucation topics. As a result, table 2 consists of only 5.2 System Based Analysis eductional accounts - see also table 3. Although users Definition 3. Assume a (multi)set S = x ,...,x is from more than one domain would yield a more re- { 1 n} partitioned into b distinct subsets Sk,1 k b such that ≤ ≤ b ∑ Sk = S k=1 | | | | where identical elements of S are placed on the same S . The plot of S versus their ranking is termed the k | k| scree plot of S. When the logarithm of Sk is used instead, then the plot is called the logscree| plot.| Definition 4. Assume a fixed set T of influence met- ric evaluation tests. Metric µ1 outperforms µ2 with respect to T if and only if µ1 achieves strictly better evaluation scores than µ2 in each test of T. This case Figure 2: Tweets and retweets per day. is denoted as µ1 µ2.
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(a) Conversational (b) Influential Figure 3: Atomic conversational and influential ranking scree plots.
(a) Conversational (b) Influential Figure 4: Atomic conversational and influential ranking logscree plots.
Definition 5. Assume a fixed set T of influence metric Taking logarithms of both sides linearizes (2) evaluation tests. Metric µ1 is at least as good as µ2 yielding with respect to T if and only if µ1 achieves 2 ln S1 0 1 strictly better evaluation score than µ in at least ln|S | ln2 1 • one test of T | 2| − ln S ln2 1 γ0 2 3 = (3) the same evaluation score with µ in the remain- |. | − . . lnα0 • . . . ing tests . . . ln S lnb 1 This case is denoted as µ1 µ2. | b| − This section outlines a method for evaluate rank- The normal equations for (3) are: ings based concepts from system theory. The analysis relies on the following properties: b b 2 b ∑k=1 ln Sk lnk ∑k=1 ln k ∑k=1 lnk γ0 − b | | = b − Property 5. Rankings in large, scale free graphs tend ∑ ln S ∑ lnk b lnα0 k=1 k k=1 to exhibit behavior which can be modelled by a Zipf | | − (4) equation which has the form
b The least squares estimation γˆLS of γ0 under this γ S = α k− 0 , α ,γ > 0, S = S (2) model is | k| 0 0 0 ∑ | k| | | k=1 b b b b ∑k=1 ln Sk lnk ∑k=1 ln Sk ∑k=1 lnk where S is the cardinality of the k-th subset of S. γˆLS = | | − | | k − b 2 b 2 | | b ∑k=1 ln k ∑k=1 ln k In this case, the data has been partitioned to b = − (5) S bins. This choice yields unbiased estimators | | For each influence metric of section 4, a Zipf model with reasonable error bounds while keeping low the has been fitted using the least squares approach which pcomputational complexity. was just described. Table 4 shows the values of γˆLS for Property 6. For most large systems γ0 belongs to the each case. Observe that the exponent estimated for the continuous interval [2,3]. atomic influence metric is the closest to the exponent
118 Evaluating Twitter Influence Ranking with System Theory
continuous range [2,3], which is the interval most ex- have been deemed as important, 4 were both atomic ponents associated with aspects of large, real world conversational and multisystemic and 2 were atomic social graphs typically belong to (Leskovec, 2011). popular.
Table 4: γˆLS for each influence metric. Table 6: Tanimoto coefficient between metrics. C M E P I C M E P I µ µ µ µ µ τ , µ µ µ µ µ · · γˆLS 1.41 1.78 1.65 1.61 1.91 µC 1 0.523 0.400 0.511 0.340 µM 0.523 1 0.017 0.194 0.403 At this point two questions arise. The first is µE 0.400 0.017 1 0.701 0.192 which of the five influence metrics reveals more infor- µP 0.511 0.194 0.701 1 0.210 mation regarding user online activity and thus identi- µI 0.340 0.403 0.192 0.210 1 fies influential individuals in a better way. The second question is, once a baseline ranking is established, how the others compare with it. From the above, the following metric ordering can The first question has been addressed by a domain be inferred: expert, who established a ground truth ranking µ∗. Ta- µI µM µC µP µE (7) ble 3 contains a complete ranking according to the do- main expert, whereas table 5 shows the percentage of Concluding, as a general remark regarding influence influential users listed in each of the ten percentiles of metrics, it should be noted that social graphs contain the rankings returned by each of the five metrics. information of inherently high order, in the sense that for a spectrum of queries, a considerable number of Table 5: Percentage of influential users. edges should be visited in order to obtain meaning- C M E P I µ∗ µ µ µ µ µ ful information. This can be at least partly attributed 50 10 22 11 32 26 to the distributed and connection oriented nature of a 50 11 7 11 7 52 graph. User influence metrics are not an exception to 0 9 33 9 8 19 this rule as influence can be in a certain sense dif- 0 5 28 7 7 6 fused through tweets, retweets and user references. 0 10 10 8 6 7 Therefore, a significant Twitter user can influence the 0 12 10 12 19 0 opinion of its neighbors but also the opinions of their 0 28 0 25 5 0 neighbors (e.g. followers of followers). Thus, influ- 0 10 0 10 6 0 ence metrics should take into account higher order 0 9 0 10 0 0 phenomena, if meaningful results are to be obtained. 0 11 0 7 0 0
Atomic conversational and atomic energetic tend to exhibit similar patterns. Moreover, they yield the 6 CONCLUSIONS AND FUTURE worst list as the influential users are scattered almost WORK uniformly across the percentiles. On the other hand, the atomic influential has the best performance. This Twitter influence ranking has been cast in a multidis- was expected since µI combines multiplicatively five ciplinary way. Five Twitter-specific functional influ- features in a nonnegative scalar, whereas the other ence metrics have been implemented in Java using the four rankings rely on a single feature. NetBeans libraries for interfacing with a Neo4j server Table 6 contains the Tanimoto coefficients be- through the Cypher API. Also, an evaluation method- tween the five influence metrics of section 4. Through ology for the influence metrics based on systems the- the five sets of ranking results, the similarity of each ory is proposed. influence metric is approximated by the Tanimoto co- Within the immediate scope of this work, research efficient defined for any two sets S1 and S2 as: can be conducted towards developing advanced func- tional rankings or hybrid structrural-functional rank- S1 S2 S1 S2 τS ,S =4 | ∩ | = | ∩ | (6) ings. The same analysis proposed in this paper should 1 2 S S S + S S S | 1 ∪ 2| | 1| | 2| − | 1 ∩ 2| be applied to Twitter subgraphs consisting of accounts There are many dissimilarities each ranking has from from multiple domains. Finally, research should in- the baseline µI. It is remarkable that each of the re- clude the development of rankings integrating the maining rankings differs in its own way. For instance, concepts of reputation and trustworthiness in social out of the 25 most atomic influential users, only 6 media.
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