Statistical physics of exchangeable sparse simple networks, multiplex networks, and simplicial complexes

Area of Science:

• Statistical physics
• Network science
• Graph theory

Background:

• Exchangeability is crucial for network ensembles, ensuring invariance upon node relabeling.
• Combining network sparsity with exchangeability presents significant theoretical challenges.
• Existing methods like exponential random graphs often rely on extensive local constraints, limiting generalizability.

Purpose of the Study:

• To propose a novel statistical physics framework for constructing exchangeable sparse network ensembles.
• To develop a Metropolis-Hastings algorithm for generating such networks.
• To extend the framework to various network types, including those with correlations and complex structures.

Main Methods:

• Development of a statistical physics model based on global constraints.
• Implementation of a Metropolis-Hastings algorithm for network generation.
• Formulation and extension of the framework for uncorrelated and correlated networks, including multiplex networks and simplicial complexes.

Main Results:

• The proposed framework successfully defines exchangeable sparse network ensembles.
• The model generates networks with heterogeneous degree distributions via global constraints.
• The framework is generalized to encompass degree correlations, directed, bipartite, multiplex networks, and simplicial complexes.

Conclusions:

• The statistical physics approach provides a general and powerful method for creating exchangeable network ensembles.
• This framework overcomes limitations of existing methods by utilizing global constraints.
• The study successfully formulates and treats exchangeable ensembles for complex network structures like simplicial complexes.