IJCsatellite IJCsatellite/cond-mat



From: Hideo Hasegawa [view email]
Date (v1): Tue, 14 Jun 2005 03:23:39 GMT   (372kb)
Date (revised v2): Wed, 15 Jun 2005 02:24:51 GMT   (372kb)

Nonextensive maximum-entropy approach to small-world networks

Authors: Hideo Hasegawa (Tokyo Gakugei Univ.)
Comments: 14 pages, 7 figures, corrected typos and refined figs
Subj-class: Disordered Systems and Neural Networks; Statistical Mechanics

The degree distribution $P(k)$ in complex networks has been obtained by maximizing the nonextensive information entropy with the three constraints: $<1>=1$, $<k>=?mu$ and $<k^2>=?rho$, where $<>$ denotes the average over $P(k)$. The distribution $P(k)$ is expressed by a generalized Gaussian (referred to as {?it $Q$-Gaussian}) which has a maximum at $k=?mu$ with a width proportional to $?sqrt{?rho-?mu^2}$, in contrast to a conventional $q$-Gaussian with a maximum at the zero value. It has been shown that $Q$-Gaussian well describes the degree distribution in small-world networks. An alternative, differential-equation approach to $Q$-Gaussian is discussed also.

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