Multicommunity weight-driven bipartite network model

H. Fan, Z. Wang, T. Ohnishi, H. Saito, and K. Aihara
Phys. Rev. E 78, 026103 – Published 8 August 2008

Abstract

Community structure and rewiring phenomena exist in many complex networks, particularly in bipartite networks. We construct a model for the degree distribution of the rewiring problem in a multicommunity weight-driven bipartite network (MCWBN). The network consists of many interconnected communities, each of which holds a bipartite graph. The bipartite graph consists of two sets of nodes. We name each node in one set a “producer” and each node in the other set a “consumer.” A weight value matrix defining the trade barrier between any two communities is used to characterize the structure of the communities, which ensures the higher preferential attachment probability in intracommunity than in intercommunity. The size of one producer is defined as the number of consumers connected to it. We find that the nonlinear dynamics of the scale of production, or the total size of all producers in each community is dependent only on the initial scale of production in each community, and independent of the distribution of the producer size. Furthermore, if the nonlinear system of the scale of production in each community is at an equilibrium state, the distribution of the producer size in each community of the MCWBN model is equivalent to that in a one-community model.

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  • Received 1 February 2007

DOI:https://doi.org/10.1103/PhysRevE.78.026103

©2008 American Physical Society

Authors & Affiliations

H. Fan1, Z. Wang2, T. Ohnishi3, H. Saito4, and K. Aihara1,4

  • 1Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-Ku, Tokyo 113-8656, Japan
  • 2College of Information Science and Technology, Donghua University, Shanghai 200051, China
  • 3Graduate School of Law and Politics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-Ku, Tokyo 113-0033, Japan
  • 4ERATO Aihara Complexity Modelling Project, JST, 45-18 Oyama, Shibuya-ku, Tokyo 151-0065, Japan

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Issue

Vol. 78, Iss. 2 — August 2008

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