Finding communities in directed networks.

To identify communities in directed networks, we propose a generalized form of modularity in directed networks by presenting the quantity LinkRank, which can be considered as the PageRank of links. This generalization is consistent with the original modularity in undirected networks and the modularity optimization methods developed for undirected networks can be directly applied to directed networks by optimizing our modified modularity. Also, a model network, which can be used as a benchmark network in further community studies, is proposed to verify our method. Our method is supposed to find communities effectively in citation- or reference-based directed networks.

[1]  Elmer S. West.  From the U. S. A. , 1965 .

[2]  J. Mogul,et al.  Computer networks and isdn systems , 1995 .

[3]  Sergey Brin,et al.  The Anatomy of a Large-Scale Hypertextual Web Search Engine , 1998, Comput. Networks.

[4]  Carl D. Meyer,et al.  Matrix Analysis and Applied Linear Algebra , 2000 .

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

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

[7]  Sergey N. Dorogovtsev,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW (Physics) , 2003 .

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

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

[10]  R. Guimerà,et al.  Modularity from fluctuations in random graphs and complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Heiko Rieger,et al.  Random walks on complex networks. , 2004, Physical review letters.

[12]  M E J Newman,et al.  Finding and evaluating community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Albert-László Barabási,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW , 2004 .

[14]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .

[15]  Roger Guimerà,et al.  Cartography of complex networks: modules and universal roles , 2005, Journal of statistical mechanics.

[16]  Leon Danon,et al.  Comparing community structure identification , 2005, cond-mat/0505245.

[17]  M E J Newman,et al.  Modularity and community structure in networks. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[18]  Alessandro Vespignani,et al.  The role of the airline transportation network in the prediction and predictability of global epidemics , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[19]  Amy Nicole Langville,et al.  Google's PageRank and beyond - the science of search engine rankings , 2006 .

[20]  E A Leicht,et al.  Mixture models and exploratory analysis in networks , 2006, Proceedings of the National Academy of Sciences.

[21]  James Hendler,et al.  Google’s PageRank and Beyond: The Science of Search Engine Rankings , 2007 .

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

[23]  R. Guimerà,et al.  Classes of complex networks defined by role-to-role connectivity profiles. , 2007, Nature physics.

[24]  Roger Guimerà,et al.  Module identification in bipartite and directed networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Sergio Gómez,et al.  Size reduction of complex networks preserving modularity , 2007, ArXiv.

[26]  M. Newman,et al.  Robustness of community structure in networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Charles Kemp,et al.  The discovery of structural form , 2008, Proceedings of the National Academy of Sciences.

[28]  S. Fortunato,et al.  Spectral centrality measures in complex networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[30]  Oleg E. Melnik,et al.  Encyclopedia of Complexity and Systems Science , 2008 .

[31]  E A Leicht,et al.  Community structure in directed networks. , 2007, Physical review letters.

[32]  H. Ohtsuki,et al.  Evolutionary dynamics and fixation probabilities in directed networks , 2008, 0812.1075.