Model and empirical study on some collaboration networks

In this paper we present an empirical study of a few practical systems described by cooperation networks, and propose a model to understand the results obtained. We study four non-social systems, which are the Bus Route Networks of Beijing and Yangzhou, the Travel Route Network of China, Huai-Yang recipes of Chinese cooked food, and a social system, which is the Collaboration Network of Hollywood Actors. In order to explain the results related to the degree distribution, act-degree distribution and act-size distribution (especially about the degree distribution, which may be better fitted using a stretched exponential distribution (SED)), we suggest a simple model to show a possible evolutionary mechanism for the emergence of such networks. The analytic and numerical results obtained from the model are in good agreement with the empirical results.

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

[2]  Nong Ye,et al.  Connectivity distribution and attack tolerance of general networks with both preferential and random attachments , 2002 .

[3]  Jie Chen,et al.  COMPLEX NETWORK PROPERTIES OF CHINESE POWER GRID , 2004 .

[4]  Camille Roth,et al.  Empiricism for descriptive social network models , 2007 .

[5]  Arnab Chatterjee,et al.  Small-world properties of the Indian railway network. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[7]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994 .

[8]  L. Sander,et al.  Diffusion-limited aggregation, a kinetic critical phenomenon , 1981 .

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

[10]  S. N. Dorogovtsev,et al.  Self-organization of collaboration networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[12]  D. Sornette,et al.  Stretched exponential distributions in nature and economy: “fat tails” with characteristic scales , 1998, cond-mat/9801293.

[13]  Massimo Marchiori,et al.  Is the Boston subway a small-world network? , 2002 .

[14]  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.

[15]  Pablo M. Gleiser,et al.  Community Structure in Jazz , 2003, Adv. Complex Syst..

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

[17]  Cai Xu,et al.  Structural Properties of US Flight Network , 2003 .

[18]  Xiangyang Zhu,et al.  STATISTICS AND DEVELOPING MODEL OF CHINESE SKYWAY NETWORK , 2004 .

[19]  Xiang Li,et al.  A local-world evolving network model , 2003 .