Article,
The Statistical Physics of Real-World Networks
CoRR, (2018)cite arxiv:1810.05095Comment: To appear on Nature Reviews Physics. The revised accepted version will be posted 6 months after publication.
Abstract
Statistical physics is the natural framework to model complex networks. In
the last twenty years, it has brought novel physical insights on a variety of
emergent phenomena, such as self-organisation, scale invariance, mixed
distributions and ensemble non-equivalence, which cannot be deduced from the
behaviour of the individual constituents. At the same time, thanks to its deep
connection with information theory, statistical physics and the principle of
maximum entropy have led to the definition of null models reproducing some
features of empirical networks, but otherwise as random as possible. We review
here the statistical physics approach for complex networks and the null models
for the various physical problems, focusing in particular on the analytic
frameworks reproducing the local features of the network. We show how these
models have been used to detect statistically significant and predictive
structural patterns in real-world networks, as well as to reconstruct the
network structure in case of incomplete information. We further survey the
statistical physics frameworks that reproduce more complex, semi-local network
features using Markov chain Monte Carlo sampling, and the models of generalised
network structures such as multiplex networks, interacting networks and
simplicial complexes.
