Scale-free property of local-world networks and their community structures

The scale-free property and community structures of complex networks formed by local events have been studied theoretically, numerically, and empirically. We showed analytically and numerically that the degree distribution function P(k) of the local-world evolving network exhibits a crossover from an exponential to power-law form by increasing the local-world size M. For M much larger than the crossover local-world size Mco, the distribution function P(k) has a power-law form for any degree k(≫1). Below Mco, however, P(k) obeys a power law for 1≪k≪kco and decays exponentially for k≫kco. The crossover size Mco and the crossover degree kco have been also elucidated. In addition, we constructed the drug prescription network (DPN) as a real local-world network, in which the local-world subsets are definitely specified, to reveal how the local-world nature affects properties of real-world networks. We found that the community structure of the DPN strongly correlates with the local worlds.

[1]  Qin Sen,et al.  A new local-world evolving network model , 2009 .

[2]  Xiaofan Wang,et al.  Generalized local-world models for weighted networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Quanyuan Jiang,et al.  A neighbourhood evolving network model , 2006 .

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

[5]  Xiaofan Wang,et al.  A new community-based evolving network model , 2007 .

[6]  Xun Zhang,et al.  Growing community networks with local events , 2009, 0902.0652.

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

[8]  Shuigeng Zhou,et al.  Local-world evolving networks with tunable clustering , 2007 .

[9]  Benjamin H. Good,et al.  Performance of modularity maximization in practical contexts. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[11]  S. Fortunato,et al.  Resolution limit in community detection , 2006, Proceedings of the National Academy of Sciences.

[12]  Tao Zhou,et al.  Local preferential attachment model for hierarchical networks , 2009 .

[13]  Santo Fortunato,et al.  Scale-free network growth by ranking. , 2006, Physical review letters.

[14]  Martin Rosvall,et al.  Maps of random walks on complex networks reveal community structure , 2007, Proceedings of the National Academy of Sciences.

[15]  戴冠中,et al.  A new local-world evolving network model , 2009 .

[16]  Santo Fortunato,et al.  Community detection in graphs , 2009, ArXiv.

[17]  K. Yakubo,et al.  Generalized strength of weighted scale-free networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Z. Di,et al.  The analysis and dissimilarity comparison of community structure , 2006 .

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

[20]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[21]  Alessandro Vespignani,et al.  Weighted evolving networks: coupling topology and weight dynamics. , 2004, Physical review letters.

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

[23]  M. Newman.  Analysis of weighted networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

[26]  Z. Di,et al.  Accuracy and precision of methods for community identification in weighted networks , 2006, physics/0607271.