DOCSLIB.ORG

Centrality Measures and Link Analysis

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Centrality Measures and Link Analysis Centrality Measures and Link Analysis Gonzalo Mateos Dept. of ECE and Goergen Institute for Data Science University of Rochester [email protected] http://www.ece.rochester.edu/~gmateosb/ February 21, 2020 Network Science Analytics Centrality Measures and Link Analysis 1 Centrality measures Centrality measures Case study: Stability of centrality measures in weighted graphs Centrality, link analysis and web search A primer on Markov chains PageRank as a random walk PageRank algorithm leveraging Markov chain structure Network Science Analytics Centrality Measures and Link Analysis 2 Quantifying vertex importance I In network analysis many questions relate to vertex importance Example I Q1: Which actors in a social network hold the `reins of power'? I Q2: How authoritative is a WWW page considered by peers? I Q3: The `knock-out' of which genes is likely to be lethal? I Q4: How critical to the daily commute is a subway station? I Measures of vertex centrality quantify such notions of importance ) Degrees are simplest centrality measures. Let's study others Network Science Analytics Centrality Measures and Link Analysis 3 Closeness centrality I Rationale: `central' means a vertex is `close' to many other vertices I Def: Distance d(u; v) between vertices u and v is the length of the shortest u − v path. Oftentimes referred to as geodesic distance I Closeness centrality of vertex v is given by 1 cCl (v) = P u2V d(u; v) ∗ I Interpret v = arg maxv cCl (v) as the most approachable node in G Network Science Analytics Centrality Measures and Link Analysis 4 Normalization, computation and limitations I To compare with other centrality measures, often normalize to [0; 1] Nv − 1 cCl (v) = P u2V d(u; v) I Computation: need all pairwise shortest path distances in G 2 ) Dijkstra's algorithm in O(Nv log Nv + Nv Ne ) time I Limitation 1: sensitivity, values tend to span a small dynamic range ) Hard to discriminate between central and less central nodes I Limitation 2: assumes connectivity, if not cCl (v) = 0 for all v 2 V ) Compute centrality indices in different components Network Science Analytics Centrality Measures and Link Analysis 5 Betweenness centrality I Rationale: `central' node is (in the path) `between' many vertex pairs I Betweenness centrality of vertex v is given by X σ(s; tjv) c (v) = Be σ(s; t) s6=t6=v2V I σ(s; t) is the total number of s − t shortest paths I σ(s; tjv) is the number of s − t shortest paths through v 2 V ∗ I Interpret v = arg maxv cBe (v) as the controller of information flow Network Science Analytics Centrality Measures and Link Analysis 6 Computational considerations I Notice that a s − t shortest path goes through v if and only if d(s; t) = d(s; v) + d(v; t) I Betweenness centralities can be naively computed for all v 2 V by: Step 1: Use Dijkstra to tabulate d(s; t) and σ(s; t) for all s; t Step 2: Use the tables to identify σ(s; tjv) for all v 3 Step 3: Sum the fractions to obtain cBe (v) for all v (O(Nv ) time) I Cubic complexity can be prohibitive for large networks I O(Nv Ne )-time algorithm for unweighted graphs in: U. Brandes, \A faster algorithm for betweenness centrality," Journal of Mathematical Sociology, vol. 25, no. 2, pp. 163-177, 2001 Network Science Analytics Centrality Measures and Link Analysis 7 Eigenvector centrality I Rationale: `central' vertex if `in-neighbors' are themselves important ) Compare with `importance-agnostic' degree centrality I Eigenvector centrality of vertex v is implicitly defined as X cEi (v) = α cEi (u) (u;v)2E I No one points to 1 5 4 I Only 1 points to 2 I Only 2 points to 3, but 2 1 6 more important than 1 I 4 as high as 5 with less links 2 3 I Links to 5 have lower rank I Same for 6 Network Science Analytics Centrality Measures and Link Analysis 8 Eigenvalue problem I Recall the adjacency matrix A and X cEi (v) = α cEi (u) (u;v)2E > I Vector cEi = [cEi (1);:::; cEi (Nv )] solves the eigenvalue problem −1 AcEi = α cEi ) Typically α−1 chosen as largest eigenvalue of A [Bonacich'87] I If G is undirected and connected, by Perron's Theorem then ) The largest eigenvalue of A is positive and simple ) All the entries in the dominant eigenvector cEi are positive −1 2 I Can compute cEi and α via O(Nv ) complexity power iterations AcEi (k) cEi (k + 1) = ; k = 0; 1;::: kAcEi (k)k Network Science Analytics Centrality Measures and Link Analysis 9 Example: Comparing centrality measures I Q: Which vertices are more central? A: It depends on the context I Each measure identifies a different vertex as most central ) None is `wrong', they target different notions of importance Network Science Analytics Centrality Measures and Link Analysis 10 4 4 Example: Comparing centrality measures I Q: Which vertices are more central? A: It depends on the context 4 4 (a)(a) (b) (b) (a)(a) (b) (b) (c)(c) (d) (d) Fig.Fig. 4.4 4.4IllustrationIllustration of (b) of (b) closeness, closeness, (c) (c) betweenness, betweenness, and and (d) (d) eigenvector eigenvector centrality centrality measures measures on on Closeness thethe graph graphBetweenness in (a). in (a). Example Example and andfiguresfigures courtesy courtesy of Ulrik of Ulrik Brandes. Brandes.Eigenvector I Small green vertices are arguably more peripheral ) Less clear how the yellow, dark blue and red vertices compare (c)(c) (d) (d) Network Science Analytics Centrality Measures and Link Analysis 11 Fig.Fig. 4.4 4.4IllustrationIllustration of of (b) (b) closeness, closeness, (c) (c) betweenness, betweenness, and and (d) (d) eigenvector eigenvector centrality centrality measures measures on on thethe graph graph in in (a). (a). Example Example and andfiguresfigures courtesy courtesy of of Ulrik Ulrik Brandes. Brandes. Case study Centrality measures Case study: Stability of centrality measures in weighted graphs Centrality, link analysis and web search A primer on Markov chains PageRank as a random walk PageRank algorithm leveraging Markov chain structure Network Science Analytics Centrality Measures and Link Analysis 12 Centrality measures robustness I Robustness to noise in network data is of practical importance I Approaches have been mostly empirical ) Find average response in random graphs when perturbed ) Not generalizable and does not provide explanations I Characterize behavior in noisy real graphs ) Degree and closeness are more reliable than betweenness I Q: What is really going on? ) Framework to study formally the stability of centrality measures I S. Segarra and A. Ribeiro, \Stability and continuity of centrality measures in weighted graphs," IEEE Trans. Signal Process., 2015 Network Science Analytics Centrality Measures and Link Analysis 13 Definitions for weighted digraphs 5 I Weighted and directed graphs G(V ; E; W ) a b ) Set V of Nv vertices 2 ) Set E ⊆ V × V of edges 3 4 ) Map W : E ! of weights in each edge R++ c I Path P(u; v) is an ordered sequence of nodes from u to v I When weights represent dissimilarities ) Path length is the sum of the dissimilarities encountered I Shortest path length sG (u; v) from u to v `−1 X sG (u; v) := min W (ui ; ui+1) P(u;v) i=0 Network Science Analytics Centrality Measures and Link Analysis 14 Stability of centrality measures I Space of graphs G(V ;E) with (V ; E) as vertex and edge set I Define the metric d(V ;E)(G; H): G(V ;E) × G(V ;E) ! R+ X d(V ;E)(G; H) := jWG (e) − WH (e)j e2E I Def: A centrality measure c(·) is stable if for any vertex v 2 V in any two graphs G; H 2 G(V ;E), then G H c (v) − c (v) ≤ KG d(V ;E)(G; H) I KG is a constant depending on G only I Stability is related to Lipschitz continuity in G(V ;E) I Independent of the definition of d(V ;E) (equivalence of norms) I Node importance should be robust to small perturbations in the graph Network Science Analytics Centrality Measures and Link Analysis 15 Degree centrality I Sum of the weights of incoming arcs X cDe (v) := W (u; v) uj(u;v)2E I Applied to graphs where the weights in W represent similarities I High cDe (v) ) v similar to its large number of neighbors Proposition 1 For any vertex v 2 V in any two graphs G; H 2 G(V ;E), we have that G H jcDe (v) − cDe (v)j ≤ d(V ;E)(G; H) i.e., degree centrality cDe is a stable measure I Can show closeness and eigenvector centralities are also stable Network Science Analytics Centrality Measures and Link Analysis 16 Betweenness centrality I Look at the shortest paths for every two nodes distinct from v ) Sum the proportion that contains node v X σ(s; tjv) c (v) := Be σ(s; t) s6=v6=t2V I σ(s; t) is the total number of s − t shortest paths I σ(s; tjv) is the number of those paths going through v Proposition 2 The betweenness centrality measure cBe is not stable Network Science Analytics Centrality Measures and Link Analysis 17 Instability of betweenness centrality I Compare the value of cBe (v) in graphs G and H G H 1 1 v 1 1 1 1 + v 1 + 1 1 1 1 1 1 1 1 1 G H cBe (v) = 9 cBe (v) = 0 H ) Centrality value cBe (v) = 0 remains unchanged for any > 0 I For small values of , graphs G and H become arbitrarily similar G H 9 = jcBe (v) − cBe (v)j ≤ KG d(V ;E)(G; H) ! 0 ) Inequality is not true for any constant KG Network Science Analytics Centrality Measures and Link Analysis 18 Stable betweenness centrality v v v v v v v I Define G =(V ; E ; W ), V =V nfvg, E =EjV v ×V v , W =W jE v ) G v obtained by deleting from G node v and edges connected to v I Stable betweenness centrality cSBe (v) X cSBe (v) := sG v (s; t) − sG (s; t) s6=v6=t2V ) Captures impact of deleting v on the shortest paths I If v is (not) in the s − t shortest path, sG v (s; t) − sG (s; t) > (=)0 ) Same notion as (traditional)
Load more

Recommended publications
  • Introduction to Network Science & Visualisation
    IFC – Bank Indonesia International Workshop and Seminar on “Big Data for Central Bank Policies / Building Pathways for Policy Making with Big Data” Bali, Indonesia, 23-26 July 2018 Introduction to network science & visualisation1 Kimmo Soramäki, Financial Network Analytics 1 This presentation was prepared for the meeting. The views expressed are those of the author and do not necessarily reflect the views of the BIS, the IFC or the central banks and other institutions represented at the meeting. FNA FNA Introduction to Network Science & Visualization I Dr. Kimmo Soramäki Founder & CEO, FNA www.fna.fi Agenda Network Science ● Introduction ● Key concepts Exposure Networks ● OTC Derivatives ● CCP Interconnectedness Correlation Networks ● Housing Bubble and Crisis ● US Presidential Election Network Science and Graphs Analytics Is already powering the best known AI applications Knowledge Social Product Economic Knowledge Payment Graph Graph Graph Graph Graph Graph Network Science and Graphs Analytics “Goldman Sachs takes a DIY approach to graph analytics” For enhanced compliance and fraud detection (www.TechTarget.com, Mar 2015). “PayPal relies on graph techniques to perform sophisticated fraud detection” Saving them more than $700 million and enabling them to perform predictive fraud analysis, according to the IDC (www.globalbankingandfinance.com, Jan 2016) "Network diagnostics .. may displace atomised metrics such as VaR” Regulators are increasing using network science for financial stability analysis. (Andy Haldane, Bank of England Executive
    [Show full text]
  • Evolving Networks and Social Network Analysis Methods And
    DOI: 10.5772/intechopen.79041 ProvisionalChapter chapter 7 Evolving Networks andand SocialSocial NetworkNetwork AnalysisAnalysis Methods and Techniques Mário Cordeiro, Rui P. Sarmento,Sarmento, PavelPavel BrazdilBrazdil andand João Gama Additional information isis available atat thethe endend ofof thethe chapterchapter http://dx.doi.org/10.5772/intechopen.79041 Abstract Evolving networks by definition are networks that change as a function of time. They are a natural extension of network science since almost all real-world networks evolve over time, either by adding or by removing nodes or links over time: elementary actor-level network measures like network centrality change as a function of time, popularity and influence of individuals grow or fade depending on processes, and events occur in net- works during time intervals. Other problems such as network-level statistics computation, link prediction, community detection, and visualization gain additional research impor- tance when applied to dynamic online social networks (OSNs). Due to their temporal dimension, rapid growth of users, velocity of changes in networks, and amount of data that these OSNs generate, effective and efficient methods and techniques for small static networks are now required to scale and deal with the temporal dimension in case of streaming settings. This chapter reviews the state of the art in selected aspects of evolving social networks presenting open research challenges related to OSNs. The challenges suggest that significant further research is required in evolving social networks, i.e., existent methods, techniques, and algorithms must be rethought and designed toward incremental and dynamic versions that allow the efficient analysis of evolving networks. Keywords: evolving networks, social network analysis 1.
    [Show full text]
  • Network Science, Homophily and Who Reviews Who in the Linux Kernel? Working Paper[+] › Open-Access at ECIS2020-Arxiv.Pdf
    Network Science, Homophily and Who Reviews Who in the Linux Kernel? Working paper[P] Open-access at http://users.abo.fi/jteixeir/pub/linuxsna/ ECIS2020-arxiv.pdf José Apolinário Teixeira Åbo Akademi University Finland # jteixeira@abo. Ville Leppänen University of Turku Finland Sami Hyrynsalmi arXiv:2106.09329v1 [cs.SE] 17 Jun 2021 LUT University Finland [P]As presented at 2020 European Conference on Information Systems (ECIS 2020), held Online, June 15-17, 2020. The ocial conference proceedings are available at the AIS eLibrary (https://aisel.aisnet.org/ecis2020_rp/). Page ii of 24 ? Copyright notice ? The copyright is held by the authors. The same article is available at the AIS Electronic Library (AISeL) with permission from the authors (see https://aisel.aisnet.org/ ecis2020_rp/). The Association for Information Systems (AIS) can publish and repro- duce this article as part of the Proceedings of the European Conference on Information Systems (ECIS 2020). ? Archiving information ? The article was self-archived by the rst author at its own personal website http:// users.abo.fi/jteixeir/pub/linuxsna/ECIS2020-arxiv.pdf dur- ing June 2021 after the work was presented at the 28th European Conference on Informa- tion Systems (ECIS 2020). Page iii of 24 ð Funding and Acknowledgements ð The rst author’s eorts were partially nanced by Liikesivistysrahasto - the Finnish Foundation for Economic Education, the Academy of Finland via the DiWIL project (see http://abo./diwil) project. A research companion website at http://users.abo./jteixeir/ECIS2020cw supports the paper with additional methodological details, additional data visualizations (plots, tables, and networks), as well as high-resolution versions of the gures embedded in the paper.
    [Show full text]
  • Network Science
    This is a preprint of Katy Börner, Soma Sanyal and Alessandro Vespignani (2007) Network Science. In Blaise Cronin (Ed) Annual Review of Information Science & Technology, Volume 41. Medford, NJ: Information Today, Inc./American Society for Information Science and Technology, chapter 12, pp. 537-607. Network Science Katy Börner School of Library and Information Science, Indiana University, Bloomington, IN 47405, USA [email protected] Soma Sanyal School of Library and Information Science, Indiana University, Bloomington, IN 47405, USA [email protected] Alessandro Vespignani School of Informatics, Indiana University, Bloomington, IN 47406, USA [email protected] 1. Introduction.............................................................................................................................................2 2. Notions and Notations.............................................................................................................................4 2.1 Graphs and Subgraphs .........................................................................................................................5 2.2 Graph Connectivity..............................................................................................................................7 3. Network Sampling ..................................................................................................................................9 4. Network Measurements........................................................................................................................11
    [Show full text]
  • Deep Generative Modeling in Network Science with Applications to Public Policy Research
    Working Paper Deep Generative Modeling in Network Science with Applications to Public Policy Research Gavin S. Hartnett, Raffaele Vardavas, Lawrence Baker, Michael Chaykowsky, C. Ben Gibson, Federico Girosi, David Kennedy, and Osonde Osoba RAND Health Care WR-A843-1 September 2020 RAND working papers are intended to share researchers’ latest findings and to solicit informal peer review. They have been approved for circulation by RAND Health Care but have not been formally edted. Unless otherwise indicated, working papers can be quoted and cited without permission of the author, provided the source is clearly referred to as a working paper. RAND’s R publications do not necessarily reflect the opinions of its research clients and sponsors. ® is a registered trademark. CORPORATION For more information on this publication, visit www.rand.org/pubs/working_papers/WRA843-1.html Published by the RAND Corporation, Santa Monica, Calif. © Copyright 2020 RAND Corporation R® is a registered trademark Limited Print and Electronic Distribution Rights This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited. Permission is given to duplicate this document for personal use only, as long as it is unaltered and complete. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial use. For information on reprint and linking permissions, please visit www.rand.org/pubs/permissions.html. The RAND Corporation is a research organization that develops solutions to public policy challenges to help make communities throughout the world safer and more secure, healthier and more prosperous.
    [Show full text]
  • Supply Network Science: Emergence of a New Perspective on a Classical Field
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Apollo Supply network science: emergence of a new perspective on a classical field Alexandra Brintrup*, Anna Ledwoch Institute for Manufacturing, Department for Engineering, University of Cambridge, Charles Babbage Road, CB1 3DD, Cambridge *[email protected] Abstract Supply networks emerge as companies procure goods from one another to produce their own products. Due to a chronic lack of data, studies on these emergent structures have long focussed on local neighbourhoods, assuming simple, chain like structures. However studies conducted since 2001 have shown that supply chains are indeed complex networks that exhibit similar organisational patterns to other network types. In this paper, we present a critical review of theoretical and model based studies which conceptualise supply chains from a network science perspective, showing that empirical data does not always support theoretical models that were developed, and argue that different industrial settings may present different characteristics. Consequently, a need that arises is the development and reconciliation of interpretation across different supply network layers such as contractual relations, material flow, financial links, and co-patenting, as these different projections tend to remain in disciplinary siloes. Other gaps include a lack of null models that show whether observed properties are meaningful, a lack of dynamical models that can inform how layers evolve and adopt to changes, and a lack of studies that investigate how local decisions enable emergent outcomes. We conclude by asking the network science community to help bridge these gaps by engaging with this important area of research.
    [Show full text]
  • Applications of Network Science to Education Research: Quantifying Knowledge and the Development of Expertise Through Network Analysis
    education sciences Commentary Applications of Network Science to Education Research: Quantifying Knowledge and the Development of Expertise through Network Analysis Cynthia S. Q. Siew Department of Psychology, National University of Singapore, Singapore 117570, Singapore; [email protected] Received: 31 January 2020; Accepted: 3 April 2020; Published: 8 April 2020 Abstract: A fundamental goal of education is to inspire and instill deep, meaningful, and long-lasting conceptual change within the knowledge landscapes of students. This commentary posits that the tools of network science could be useful in helping educators achieve this goal in two ways. First, methods from cognitive psychology and network science could be helpful in quantifying and analyzing the structure of students’ knowledge of a given discipline as a knowledge network of interconnected concepts. Second, network science methods could be relevant for investigating the developmental trajectories of knowledge structures by quantifying structural change in knowledge networks, and potentially inform instructional design in order to optimize the acquisition of meaningful knowledge as the student progresses from being a novice to an expert in the subject. This commentary provides a brief introduction to common network science measures and suggests how they might be relevant for shedding light on the cognitive processes that underlie learning and retrieval, and discusses ways in which generative network growth models could inform pedagogical strategies to enable meaningful long-term conceptual change and knowledge development among students. Keywords: education; network science; knowledge; learning; expertise; development; conceptual representations 1. Introduction Cognitive scientists have had a long-standing interest in quantifying cognitive structures and representations [1,2]. The empirical evidence from cognitive psychology and psycholinguistics demonstrates that the structure of cognitive systems influences the psychological processes that operate within them.
    [Show full text]
  • Social Network Analysis in Practice
    Social Network Analysis in Practice Projektseminar WiSe 2018/19 Tim Repke, Dr. Ralf Krestel Social Network Analysis in Practice Tim Repke 17.10.2018 2 https://digitalpresent.tagesspiegel.de/afd About Me Information Extraction and Study abroad Data Visualisation Natural Language Processing and Business Text Mining Communication Work in London Analysis Write master‘s Write bachelor‘s Enrol at HUB thesis (Web IE) thesis (TOR) Begin PhD at HPI Social Network Analysis in Practice Tim Repke git log --since=2010 17.10.2018 Student Receive M.Sc. Computer Science assistant Receive B.Sc. 3 Computer Science What You Learn in this Seminar ■ Overview of topics in Social Network Analysis ■ Deep understanding of one aspect ■ Explore heterogeneous data ■ How to find, implement, and reproduce research papers ■ How to write a research abstract Social Network Analysis in Practice Tim Repke 17.10.2018 4 Schedule Paper Exploration Write and “Data Science” Review Paper February & March Overview Talks December SNA in Practice October & June January & February Social Seminar Project Network Analysis in Practice Tim Repke 17.10.2018 5 Schedule Paper Exploration Write and “Data Science” Review Paper February & March Overview Talks December SNA in Practice October & June January & February Social Seminar Project Network Analysis in Practice Tim Repke 17.10.2018 6 Schedule (pt. 1) Overview Talks Date Topics 17.10.2018 Introduction 24.10.2018 31.10.2018 Introduction to Social Network Data Reformationstag 07.11.2018 . Data acquisition and preparation . Data interpretation Introduction to Measuring Graphs . Node/dyad-level metrics 14.11.2018 . Dyad/group-level metrics . Interpreting metrics Introduction to Advanced Analysis Social .
    [Show full text]
  • Social Network Analysis: Homophily
    Social Network Analysis: homophily Donglei Du ([email protected]) Faculty of Business Administration, University of New Brunswick, NB Canada Fredericton E3B 9Y2 Donglei Du (UNB) Social Network Analysis 1 / 41 Table of contents 1 Homophily the Schelling model 2 Test of Homophily 3 Mechanisms Underlying Homophily: Selection and Social Influence 4 Affiliation Networks and link formation Affiliation Networks Three types of link formation in social affiliation Network 5 Empirical evidence Triadic closure: Empirical evidence Focal Closure: empirical evidence Membership closure: empirical evidence (Backstrom et al., 2006; Crandall et al., 2008) Quantifying the Interplay Between Selection and Social Influence: empirical evidence—a case study 6 Appendix A: Assortative mixing in general Quantify assortative mixing Donglei Du (UNB) Social Network Analysis 2 / 41 Homophily: introduction The material is adopted from Chapter 4 of (Easley and Kleinberg, 2010). "love of the same"; "birds of a feather flock together" At the aggregate level, links in a social network tend to connect people who are similar to one another in dimensions like Immutable characteristics: racial and ethnic groups; ages; etc. Mutable characteristics: places living, occupations, levels of affluence, and interests, beliefs, and opinions; etc. A.k.a., assortative mixing Donglei Du (UNB) Social Network Analysis 4 / 41 Homophily at action: racial segregation Figure: Credit: (Easley and Kleinberg, 2010) Donglei Du (UNB) Social Network Analysis 5 / 41 Homophily at action: racial segregation Credit: (Easley and Kleinberg, 2010) Figure: Credit: (Easley and Kleinberg, 2010) Donglei Du (UNB) Social Network Analysis 6 / 41 Homophily: the Schelling model Thomas Crombie Schelling (born 14 April 1921): An American economist, and Professor of foreign affairs, national security, nuclear strategy, and arms control at the School of Public Policy at University of Maryland, College Park.
    [Show full text]
  • Networks in Cognitive Science
    1 Networks in Cognitive Science Andrea Baronchelli1,*, Ramon Ferrer-i-Cancho2, Romualdo Pastor-Satorras3, Nick Chater4 and Morten H. Christiansen5,6 1 Laboratory for the Modeling of Biological and Socio-technical Systems, Northeastern University, Boston, MA 02115, USA 2 Complexity & Quantitative Linguistics Lab, TALP Research Center, Departament de Llenguatges i Sistemes Informàtics. Universitat Politècnica de Catalunya, Campus Nord, Edifici Omega, E-08034 Barcelona, Spain 3 Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord B4, E-08034 Barcelona, Spain 4Behavioural Science Group, Warwick Business School, University of Warwick, Coventry, CV4 7AL, UK 5 Department of Psychology, Cornell University, Uris Hall, Ithaca, NY 14853, USA 6 Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA *Corresponding author: email [email protected] 2 Abstract Networks of interconnected nodes have long played a key role in cognitive science, from artificial neural networks to spreading activation models of semantic memory. Recently, however, a new Network Science has been developed, providing insights into the emergence of global, system-scale properties in contexts as diverse as the Internet, metabolic reactions or collaborations among scientists. Today, the inclusion of network theory into cognitive sciences, and the expansion of complex systems science, promises to significantly change the way in which the organization and dynamics of cognitive and behavioral processes are understood. In this paper, we review recent contributions of network theory at different levels and domains within the cognitive sciences. 3 Humans have more than 1010 neurons and between 1014 and 1015 synapses in their nervous system [1]. Together, neurons and synapses form neural networks, organized into structural and functional sub-networks at many scales [2].
    [Show full text]
  • TELCOM2125: Network Science and Analysis
    School of Information Sciences University of Pittsburgh TELCOM2125: Network Science and Analysis Konstantinos Pelechrinis Spring 2015 Figures are taken from: M.E.J. Newman, “Networks: An Introduction” CHAPTER 1 INTRODUCTION A short introduction to networks and why we study them A NETWORK is, in its simplest form, a collection of points joined together in pairs by lines. In the jargon of the field the points are referred to as vertices1 or nodes and the lines are referred to as What is a network?edges . Many objects of interest in the physical, biological, and social sciences can be thought of as networks and, as this book aims to show, thinking of them in this way can often lead to new and useful insights. We begin, in this introductory chapter, with a discussion of why we are interested in networks l A collection of pointsand joined a brief description together of some in specpairsific networks by lines of note. All the topics in this chapter are covered in greater depth elsewhere in the book. § Points that will be joined together depends on the context ü Points à Vertices, nodes, actors … ü Lines à Edges l There are many systems of interest that can be modeled as networks A small network composed of eight vertices and ten edges. § Individual parts linked in some way ü Internet o A collection of computers linked together by data connections ü Human societies o A collection of people linked by acquaintance or social interaction 2 Why are we interested in networks? l While the individual components of a system (e.g., computer machines, people etc.) as well as the nature of their interaction is important, of equal importance is the pattern of connections between these components § These patterns significantly affect the performance of the underlying system ü The patterns of connections in the Internet affect the routes packets travel through ü Patterns in a social network affect the way people obtain information, form opinions etc.
    [Show full text]
  • EDITORIAL What Is Network Science?
    Network Science 1 (1): 1–15, 2013. c Cambridge University Press 2013 1 doi:10.1017/nws.2013.2 EDITORIAL What is network science? ULRIK BRANDES Department of Computer and Information Science, University of Konstanz, Germany (e-mail:)[email protected]) GARRY ROBINS Melbourne School of Psychological Sciences, University of Melbourne, Australia (e-mail:)[email protected]) ANN Mc CRANIE Department of Sociology, Indiana University Bloomington, USA (e-mail:)[email protected]) STANLEY WASSERMAN Departments of Psychological and Brain Science and Statistics, Indiana University Bloomington, USA (e-mail:)[email protected]) Abstract This is the beginning of Network Science. The journal has been created because network science is exploding. As is typical for a field in formation, the discussions about its scope, contents, and foundations are intense. On these first few pages of the first issue of our new journal, we would like to share our own vision of the emerging science of networks. 1 Is there a science of networks? Whether there is or is not a science of networks, and what should be the focus of such a science, may appear to be academic questions. We use this prominent place to argue the following three statements: • These questions are more relevant than they seem at first glance. • The answers are less obvious than have been suggested. • The future of network science is bright. Of course, the editors of a new scientific journal are going to predict that the future of their science is bright. Cambridge University Press is betting that it is. We do also think, however, that the field is still in formation and that its essential shaping is taking place right now.
    [Show full text]