Social Network Theory and Applications Leonid E. Zhukov School of Applied Mathematics and Information Science National Research University Higher School of Economics 13.01.2014 Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 1 / 35
Class Technicalities 10 lectures Online lectures: Fuze Meeting (FuzeBox.com) Website: http://www.leonidzhukov.net/hse/2014/socialnetworks My email: lzhukov@hse.ru Programming: Matlab (Octave), R, Python, Matlab libraries: MatlabBGL, GraphViz (graphviz4matlab, graphviz) R libraries: igraph, statnet Python libraries: NetworkX, igraph Visusualization: yed, Gephi Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 2 / 35
Course outline Networks structure Networks formation Networks processes Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 3 / 35
Social Networks Sociology Mathematics Computer Science Statistical Physics Economics Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 4 / 35
Terminolgy network = graph nodes = vertices, actors links = edges, relations clusters = communities Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 5 / 35
Complex networks Networks = nodes + edges not regular, but not random complex (nontrivial) topolgy scale-free networks universal properties everywhere independent agents (?) Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 6 / 35
Examples: Internet Barrett Lyon, OPTE.org, class C networks Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 7 / 35
Examples: Political blogs Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 8 / 35
Examples: Twitter Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 9 / 35
Examples: Finance Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 10 / 35
Examples: Transportation Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 11 / 35
Examples: Biology Protein-protein interactions Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 12 / 35
Examples: Organization Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 13 / 35
Examples: Facebook communities tructure Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 14 / 35
Examples: Facebook Social graph 500mln people, Paul Butler, 2010 Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 15 / 35
Graphs and Networks Graph G(V, E), V - vertices, m = V, E - edges, n = E Directed, undirected, simple (no loops), weighted Connected if every pair of vertices is connected Connected component - maximal connected subgraph Path - sequence of edges that connects sequence of vertices (simple path, no repeated vertices) Geodesic distance - shortest path, l Graph diameter D- largest shortest path. Node degree k i - number of incedent edges ( number of nearest neighbours) Degree distribution P(k) - fraction of nodes with degree k Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 16 / 35
Network represenation Graph G(n, m), adjacency matrix A ij, edge i j Storage: - adjacency list - sparse matrix Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 17 / 35
Complex network Power law degree distribution: heavy tail (long tail) distributions Small diameter and average path length: "small world" Dense local structure, high transitivity/clustering coefficient Giant connected component Hierachical structure Local community (cluster) structure Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 18 / 35
Long tail Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 19 / 35
Power law Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 20 / 35
Power law Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 21 / 35
High clustering Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 22 / 35
Giant connected component Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 23 / 35
Six degrees of separation Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 24 / 35
Six degrees of separation Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 25 / 35
Small world "The small-world problem". Stanley Milgram, 1967 "An experimental study of the small world problem J. Travers, S. Milgram, 1969 Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 26 / 35
Stanely Milgram s 1969 experiment 296 volunteers, 217 sent 196 in Nebraska (1300 miles) 100 in Boston (25 miles) Target in Boston Name, address, occupation, job, hometowm Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 27 / 35
Stanely Milgram s 1969 experiment Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 28 / 35
Stanely Milgram s 1969 experiment Reached the target N = 64, 29% Average chain length <L> = 5.2 Channeles: hometown <L> = 6.1 Business contacts <L> = 4.6 From Boston <L> = 4.4 From Nebraska <l> = 5.7 Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 29 / 35
Small world Email graph: D. Watts (2001), 48,000 senders, < L > 6 MSN Messenger graph: J. Lescovec et al (2007), 240mln users, < L > 6.6 Facebook graph: L. Backstrom et al (2012), 721 mln users, < L > 4.74 Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 30 / 35
Cayley tree Bethe lattice: infinite cycle free graph where every node connect to z neighbours - coordination number per shell N k = z(z 1) k 1 total N = 1 + L 1 z(z 1)k 1 Estimates: z L = N, L = log N/ log z N 6.7 bln, z = 50 friends, L 5.8. Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 31 / 35
Lectures Module 3: 1 Introduction to complex networks 2 Power law distributions 3 Random graphs 4 Dynamical growth models 5 Node centrality metrics 6 Link analysis 7 Structural equivalence and block structure 8 Network motifs 9 Network communities 10 Network visualization Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 32 / 35
References Scale free networks. A.-L. Barabási, E. Bonabeau, Scientific American 288, 50-59 (2003) Scale-Free Networks: A Decade and Beyond. A.-L. Barabási, Science 325, 412-413 (2009) The Physics of Networks. Mark Newman, Physics Today, November 2008, pp. 33 38. Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 33 / 35
Reviews Statistical mechanics of complex networks, R. Albert and A-L. Barabasi, Rev. Mod. Phys. 74, 47, 2002 The Structure and Function of Complex Networks, M. E. J. Newman, SIAM Review, 45, pp 167-256, 2003 Evolution of Networks, S. N. Dorogovtsev and J. F. F. Mendes, Adv. Phys., pp 1079-1187, 2002 Complex networks: Structure and dynamics, S. Boccaletti et al., Physics Reports, Volume 424, Issue 4-5, p. 175-308, 2006 Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 34 / 35
Textbooks "Networks: An Introduction". Mark Newman. Oxford University Press, 2010. "Social and Economic Networks". Matthew O. Jackson. Princeton University Press, 2010. "Networks, Crowds, and Markets: Reasoning About a Highly Connected World". David Easley and John Kleinberg, Cambridge University Press 2010. "Social Network Analysis. Methods and Applications". Stanley Wasserman and Katherine Faust, Cambridge University Press, 1994 Leonid E. Zhukov (HSE) Lecture 1 13.01.2014 35 / 35