Nonextensive aspects of small-world networks

Hideo Hasegawa

Physica A: Statistical Mechanics and its Applications, 2006, vol. 365, issue 2, 383-401

Abstract: Nonextensive aspects of the degree distribution in Watts–Strogatz (WS) small-world networks, PSW(k), have been discussed in terms of a generalized Gaussian (referred to as Q-Gaussian) which is derived by the three approaches: the maximum-entropy method (MEM), stochastic differential equation (SDE), and hidden-variable distribution (HVD). In MEM, the degree distribution PQ(k) in complex networks has been obtained from Q-Gaussian by maximizing the nonextensive information entropy with constraints on averages of k and k2 in addition to the normalization condition. In SDE, Q-Gaussian is derived from Langevin equations subject to additive and multiplicative noises. In HVD, Q-Gaussian is made by a superposition of Gaussians for random networks with fluctuating variances, in analogy to superstatistics. Interestingly, a singlePQ(k) may describe, with an accuracy of |PSW(k)-PQ(k)|≲10-2, main parts of degree distributions of SW networks, within which about 96–99% of all k states are included. It has been demonstrated that the overall behavior of PSW(k) including its tails may be well accounted for if the k-dependence is incorporated into the entropic index in MEM, which is realized in microscopic Langevin equations with generalized multiplicative noises.

Keywords: Nonextensive statistics; Small-world networks; Information entropy (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:365:y:2006:i:2:p:383-401

DOI: 10.1016/j.physa.2005.10.004

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