Abstract

New entropy measures have been recently introduced for the quantification of the complexity of networks. Most of these entropy measures apply to static networks or to dynamical processes defined on static complex networks. In this paper we define the entropy rate of growing network models. This entropy rate quantifies how many labeled networks are typically generated by the growing network models. We analytically evaluate the difference between the entropy rate of growing tree network models and the entropy of tree networks that have the same asymptotic degree distribution. We find that the growing networks with linear preferential attachment generated by dynamical models are exponentially less than the static networks with the same degree distribution for a large variety of relevant growing network models. We study the entropy rate for growing network models showing structural phase transitions including models with nonlinear preferential attachment. Finally, we bring numerical evidence that the entropy rate above and below the structural phase transitions follows a different scaling with the network size.

Notes

Originally published in Physical Review E v.84 (2011): 066113. DOI: 10.1103/PhysRevE.84.066113

Keywords

entropy measures, entropy rate, growing network models, tree networks

Subject Categories

Entropy

Disciplines

Physics | Plasma and Beam Physics

Publisher

American Physical Society

Publication Date

12-16-2011

Rights Information

Copyright (2011) American Physical Society.

Rights Holder

American Physical Society

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