Weighted networks of scientific communication: the measurement and topological role of weight

In order to take the weight of connection into consideration and to find a natural measurement of weight, we have collected papers in Econophysics and constructed a network of scientific communication to integrate idea transportation among econophysicists by collaboration, citation and personal discussion. Some basic statistics such as weight per degree are discussed in Fan et al. J. Mod. Phys. B (17–19) (2004) 2505. In this paper, by including the papers published recently, further statistical results for the network are reported. Clustering coefficient of weighted networks is introduced and empirically studied in this network. We also compare the typical statistics on this network under different weight assignments, including random and inverse weight. The conclusion from weight-redistributed network is helpful to the investigation of the topological role of weight.

[1]  Guido Caldarelli,et al.  Universal scaling relations in food webs , 2003, Nature.

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

[3]  R. Mantegna,et al.  Zipf plots and the size distribution of firms , 1995 .

[4]  A. Barabasi,et al.  Weighted evolving networks. , 2001, Physical review letters.

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

[6]  John Sutton,et al.  The Variance of Firm Growth Rates: The Scaling Puzzle , 2001 .

[7]  Rosario N. Mantegna,et al.  Book Review: An Introduction to Econophysics, Correlations, and Complexity in Finance, N. Rosario, H. Mantegna, and H. E. Stanley, Cambridge University Press, Cambridge, 2000. , 2000 .

[8]  A. Vespignani,et al.  The architecture of complex weighted networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[9]  Y. Lai,et al.  Characterization of weighted complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  A.-L. Barabasi,et al.  Minimum spanning trees of weighted scale-free networks , 2004 .

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

[12]  Massimo Marchiori,et al.  Economic small-world behavior in weighted networks , 2003 .

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

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

[15]  L. Katz,et al.  PROBABILITY DISTRIBUTIONS OF RANDOM VARIABLES ASSOCIATED WITH A STRUCTURE OF THE SAMPLE SPACE OF SOCIOMETRIC INVESTIGATIONS , 1957 .

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

[18]  Leo Egghe,et al.  a Measure for the Cohesion of Weighted Networks , 2003, J. Assoc. Inf. Sci. Technol..

[19]  P L Krapivsky,et al.  Weight-driven growing networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Liang Gao,et al.  Network of Econophysicists: a weighted network to investigate the development of Econophysics , 2004 .

[21]  S. Redner.  How popular is your paper? An empirical study of the citation distribution , 1998, cond-mat/9804163.

[22]  The variance of corporate growth rates , 2003 .

[23]  M. Potters,et al.  Theory of Financial Risk , 1997 .

[24]  K. Goh,et al.  Optimal transport in weighted complex networks , 2004 .