Multi-component static model for social networks

Abstract.The static model was introduced to generate a scale-free network. In the model, N number of vertices are present from the beginning. Each vertex has its own weight, representing how much the vertex is influential in a system. The static model, however, is not relevant, when a complex network is composed of many modules such as communities in social networks. An individual may belong to more than one community and has distinct weights for each community. Thus, we generalize the static model by assigning a q-component weight on each vertex. We first choose a component $(\mu)$ among the q components at random and a pair of vertices is linked with a color μ according to their weights of the component $(\mu)$ as in the static model. A (1-f) fraction of the entire edges is connected following this way. The remaining fraction f is added with (q + 1)-th color as in the static model but using the maximum weights among the q components each individual has. The social activity with such maximum weights is an essential ingredient to enhance the assortativity coefficient as large as the ones of real social networks.

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

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

[3]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[4]  Joao Antonio Pereira,et al.  Linked: The new science of networks , 2002 .

[5]  K. Goh,et al.  Universal behavior of load distribution in scale-free networks. , 2001, Physical review letters.

[6]  A. Barabasi,et al.  Evolution of the social network of scientific collaborations , 2001, cond-mat/0104162.

[7]  M E J Newman,et al.  Identity and Search in Social Networks , 2002, Science.

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

[9]  Fan Chung Graham,et al.  The Diameter of Sparse Random Graphs , 2001, Adv. Appl. Math..

[10]  S. N. Dorogovtsev,et al.  Evolution of networks , 2001, cond-mat/0106144.

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

[12]  M. A. Muñoz,et al.  Scale-free networks from varying vertex intrinsic fitness. , 2002, Physical review letters.

[13]  R Pastor-Satorras,et al.  Dynamical and correlation properties of the internet. , 2001, Physical review letters.

[14]  M. Newman.  Properties of highly clustered networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Mark S. Granovetter.  The Strength of Weak Ties , 1973, American Journal of Sociology.

[16]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

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

[18]  S H Strogatz,et al.  Random graph models of social networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

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

[20]  M Girvan,et al.  Structure of growing social networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Lada A. Adamic,et al.  Internet: Growth dynamics of the World-Wide Web , 1999, Nature.

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

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