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Effect of Coagulation of Nodes in an Evolving Complex Network

Wataru Miura, Hideki Takayasu, and Misako Takayasu
Phys. Rev. Lett. 108, 168701 – Published 16 April 2012

Abstract

We propose a new type of stochastic network evolution model based on annihilation, creation, and coagulation of nodes, together with the preferential attachment rule. The system reaches a unique quasistatistically steady state in which the distribution of links follows a power law, lifetime of nodes follows an exponential distribution, and the mean number of links grows exponentially with time. The master equation of the model is solved analytically by applying Smoluchowski’s coagulation equation for aerosols. The results indicate that coagulation of nodes in complex networks and mean field analysis of aerosols are similar in both the growth dynamics with irreversible processes and in the steady state statistics. We confirm that the basic properties of the model are consistent with the empirical results of a business transaction network having about 1×106 firms.

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  • Received 17 November 2011

DOI:https://doi.org/10.1103/PhysRevLett.108.168701

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

© 2012 American Physical Society

Authors & Affiliations

Wataru Miura1, Hideki Takayasu2,3, and Misako Takayasu1

  • 1Department of Computational Intelligence and Systems Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, 4259-G3-52, Nagatsuta-cho, Midori-ku, Yokohama 226-8503, Japan
  • 2Sony Computer Science Laboratories, 3-14-13, Higashigotanda, Shinagawa-ku, Tokyo 141-0022, Japan
  • 3Meiji Institute of Advanced Study of Mathematical Sciences, Meiji University, 1-1-1 Higashimita, Tama-ku, Kawasaki 214-8571, Japan

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Vol. 108, Iss. 16 — 20 April 2012

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