A statistical mechanics approach for scale-free networks and finite-scale networks

Abstract

We present a statistical mechanics approach for the description of complex networks. We first define an energy and an entropy associated to a degree distribution which have a geometrical interpretation. Next we evaluate the distribution which extremize the free energy of the network. We find two important limiting cases: a scale-free degree distribution and a finite-scale degree distribution. The size of the space of allowed simple networks given these distribution is evaluated in the large network limit. Results are compared with simulations of algorithms generating these networks.

arXiv comment(6 pages, 5 figures)

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Cited by in corpus (8)

• The entropy of network ensembles
• The entropy of randomized network ensembles
• Determination of multifractal dimensions of complex networks by means of the sandbox algorithm
• Optimization in Networks
• Classical Information Theory of Networks
• Approaching the thermodynamic limit in equilibrated scale-free networks
• Catching homologies by geometric entropy
• Complex distributions emerging in filtering and compression