Generative model for feedback networks

Douglas R. White, Nataša Kejžar, Constantino Tsallis, Doyne Farmer, and Scott White
Phys. Rev. E 73, 016119 – Published 18 January 2006

Abstract

We propose a model for network formation and study some of its statistical properties. The motivation for the model comes from the growth of several kinds of real networks (i.e., kinship and trading networks, networks of corporate alliances, networks of autocatalytic chemical reactions). These networks grow either by establishing closer connections by adding links in the existing network or by adding new nodes. A node in these networks lacks the information of the entire network. In order to establish a closer connection to other nodes it starts a search in the neighboring part of the network and waits for a possible feedback from a distant node that received the “searching signal.” Our model imitates this behavior by growing the network via the addition of a link that creates a cycle in the network or via the addition of a new node with a link to the network. The forming of a cycle creates feedback between the two ending nodes. After choosing a starting node, a search is made for another node at a suitable distance; if such a node is found, a link is established between this and the starting node, otherwise (such a node cannot be found) a new node is added and is linked to the starting node. We simulate this algorithm and find that we cannot reject the hypothesis that the empirical degree distribution is a q-exponential function, which has been used to model long-range processes in nonequilibrium statistical mechanics.

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  • Received 30 July 2005

DOI:https://doi.org/10.1103/PhysRevE.73.016119

©2006 American Physical Society

Authors & Affiliations

Douglas R. White*

  • Institute of Mathematical Behavioral Sciences, University of California Irvine, Irvine, California 92697, USA

Nataša Kejžar*

  • Faculty of Social Sciences, University of Ljubljana, Kardeljeva ploščad 5, 1000 Ljubljana, Slovenia

Constantino Tsallis*

  • Centro Brasileiro de Pesquisas Físicas, Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil

Doyne Farmer

  • Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA

Scott White

  • School of Information and Computer Science, University of California Irvine, Irvine, California 92697, USA

  • *Also at Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA.

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Vol. 73, Iss. 1 — January 2006

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