A random graph generation algorithm for the analysis of social networks

Social network analysis (SNA) is a rapidly growing field with numerous applications in industry and government. However, the field still lacks means to generate random social networks with certain desired properties, thus inhibiting their ability to test new SNA algorithms and metrics. Available random graph generation algorithms suffer from tendencies to generate disconnected graphs and sometimes induce undesirable network properties. In this paper, we present an algorithm, the prescribed node degree, connected graph (PNDCG) algorithm, designed to generate weakly connected social networks. Extensions to the PNDCG algorithm allow one to create random graphs that control the clustering coefficient and degree correlation within the generated networks. Empirical test results demonstrate the capability of the PNDCG algorithm to produce networks with the desired properties.

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

[2]  M. Newman,et al.  Why social networks are different from other types of networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  R. Deckro,et al.  Modeling and Analysis of Clandestine Networks , 2012 .

[4]  W. Zachary,et al.  An Information Flow Model for Conflict and Fission in Small Groups , 1977, Journal of Anthropological Research.

[5]  Paul Erdös,et al.  On random graphs, I , 1959 .

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

[7]  Hsinchun Chen,et al.  The topology of dark networks , 2008, Commun. ACM.

[8]  Beom Jun Kim,et al.  Growing scale-free networks with tunable clustering. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  V. Eguíluz,et al.  Growing scale-free networks with small-world behavior. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[11]  Tao Zhou,et al.  Growing scale-free small-world networks with tunable assortative coefficient , 2006 .

[12]  A. Vázquez,et al.  Network clustering coefficient without degree-correlation biases. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  S. A. Choudum.  A simple proof of the Erdos-Gallai theorem on graph sequences , 1986, Bulletin of the Australian Mathematical Society.

[14]  Sara E. Sterling.  Aggregation Techniques to Characterize Social Networks , 2012 .

[15]  Carlo Morselli,et al.  Law-Enforcement Disruption of a Drug Importation Network , 2006 .

[16]  Terrill L. Frantz,et al.  A Formal Characterization of Cellular Networks , 2005 .

[17]  Uri Alon,et al.  Uniform generation of random graphs with arbitrary degree sequences , 2003 .

[18]  M. R. Rao,et al.  Combinatorial Optimization , 1992, NATO ASI Series.

[19]  Stephen G. Nash,et al.  Guidelines for reporting results of computational experiments. Report of the ad hoc committee , 1991, Math. Program..

[20]  César A. Hidalgo,et al.  Scale-free networks , 2008, Scholarpedia.

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

[22]  John M. Roberts.  Simple methods for simulating sociomatrices with given marginal totals , 2000, Soc. Networks.

[23]  M E J Newman.  Assortative mixing in networks. , 2002, Physical review letters.

[24]  J. Hopcroft,et al.  Are randomly grown graphs really random? , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  J. Hamill.  Analysis of Layered Social Networks , 2012 .

[26]  V. Eguíluz,et al.  Highly clustered scale-free networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.