Name
Abstract | ||
|---|---|---|
In the past 15 years, statistical physics has been successful as a framework for modelling complex networks. On the theoretical side, this approach has unveiled a variety of physical phenomena, such as the emergence of mixed distributions and ensemble non-equivalence, that are observed in heterogeneous networks but not in homogeneous systems. At the same time, thanks to the deep connection between the principle of maximum entropy and information theory, statistical physics has led to the definition of null models for networks that reproduce features of real-world systems but that are otherwise as random as possible. We review here the statistical physics approach and the null models for complex networks, focusing in particular on analytical frameworks that reproduce local network features. We show how these models have been used to detect statistically significant structural patterns in real-world networks and to reconstruct the network structure in cases of incomplete information. We further survey the statistical physics models that reproduce more complex, semilocal network features using Markov chain Monte Carlo sampling, as well as models of generalized network structures, such as multiplex networks, interacting networks and simplicial complexes. This Review describes advances in the statistical physics of complex networks and provides a reference for the state of the art in theoretical network modelling and applications to real-world systems for pattern detection and network reconstruction. Key pointsStatistical physics is a powerful framework to explain properties of complex networks, modelled as systems of heterogeneous entities whose degrees of freedom are their interactions rather than their states.The statistical physics of complex networks has brought theoretical insights into physical phenomena that are different in heterogeneous networks than in homogeneous systems.From an applied perspective, statistical physics defines null models for real-world networks that reproduce local features but are otherwise as random as possible.These models have been used, on the one hand, to detect statistically significant patterns in real-world networks and, on the other, to infer the network structure when information is incomplete.These applications are particularly useful in the current information age to make consistent inference from huge streams of continuously produced, high-dimensional, noisy data.The statistical mechanics approach has also been extended using numerical techniques to reproduce semilocal network features and, more recently, to encompass structures such as multilayer networks and simplicial complexes. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1038/s42254-018-0002-6 | NATURE REVIEWS PHYSICS |
Field | DocType | Volume |
Information theory,Statistical physics,Homogeneous,Local area network,Complex network,Heterogeneous network,Principle of maximum entropy,Complete information,Mathematics,Network structure | Journal | 1 |
Issue | ISSN | Citations |
1 | Nature Reviews Physics 1(1), 58-71 (2019) | 7 |
PageRank | References | Authors |
0.64 | 27 | 6 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Giulio Cimini | 1 | 126 | 13.77 |
| Tiziano Squartini | 2 | 67 | 11.86 |
| Fabio Saracco | 3 | 14 | 2.57 |
| Diego Garlaschelli | 4 | 90 | 18.49 |
| Andrea Gabrielli | 5 | 70 | 7.82 |
| Guido Caldarelli | 6 | 382 | 40.76 |