Random graph models of social networks

We describe some new exactly solvable models of the structure of social networks, based on random graphs with arbitrary degree distributions. We give models both for simple unipartite networks, such as acquaintance networks, and bipartite networks, such as affiliation networks. We compare the predictions of our models to data for a number of real-world social networks and find that in some cases, the models are in remarkable agreement with the data, whereas in others the agreement is poorer, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph.

[1]  John Guare,et al.  Six Degrees of Separation: A Play , 1990 .

[2]  John Scott.  Social Network Analysis , 1988 .

[3]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[4]  Fan Chung Graham,et al.  A random graph model for massive graphs , 2000, STOC '00.

[5]  M. Newman,et al.  Random graphs with arbitrary degree distributions and their applications. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  J. Galaskiewicz,et al.  Interorganizational resource networks: Formal patterns of overlap , 1978 .

[7]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[8]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[9]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[10]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[11]  Cohen,et al.  Resilience of the internet to random breakdowns , 2000, Physical review letters.

[12]  M. Kochen,et al.  Contacts and influence , 1978 .

[13]  J. Weizenbaum,et al.  Social science research. , 1970, Science.

[14]  M. Newman,et al.  Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  S. Redner.  How popular is your paper? An empirical study of the citation distribution , 1998, cond-mat/9804163.

[16]  M E Newman,et al.  Scientific collaboration networks. I. Network construction and fundamental results. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  M. Newman.  Clustering and preferential attachment in growing networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[19]  H E Stanley,et al.  Classes of small-world networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[20]  D. Fell,et al.  The small world of metabolism , 2000, Nature Biotechnology.

[21]  Sharon L. Milgram,et al.  The Small World Problem , 1967 .

[22]  M. Newman,et al.  The structure of scientific collaboration networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[23]  D S Callaway,et al.  Network robustness and fragility: percolation on random graphs. , 2000, Physical review letters.

[24]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[25]  Bruce A. Reed,et al.  The Size of the Giant Component of a Random Graph with a Given Degree Sequence , 1998, Combinatorics, Probability and Computing.

[26]  John Scott.  What is social network analysis , 2010 .

[27]  Bruce A. Reed,et al.  A Critical Point for Random Graphs with a Given Degree Sequence , 1995, Random Struct. Algorithms.