Statistical-mechanical approach to subgraph centrality in complex networks

TL;DR

This paper introduces a statistical-mechanical framework for analyzing subgraph centrality in complex networks, linking spectral graph theory with thermodynamic concepts to understand network structure and dynamics.

Contribution

It develops a novel approach interpreting subgraph centrality as a network partition function, connecting spectral properties with thermodynamic quantities.

Findings

Relates network entropy, energy, and free energy to structure and dynamics.

Analyzes models of network growth and real-world biological networks.

Identifies critical coupling and cohesiveness in complex networks.

Abstract

We interpret the subgraph centrality as the partition function of a network. The entropy, the internal energy and the Helmholtz free energy are defined for networks and molecular graphs on the basis of graph spectral theory. Various relations of these quantities to the structure and the dynamics of the complex networks are discussed. They include the cohesiveness of the network and the critical coupling of coupled phase oscillators. We explore several models of network growing/evolution as well as real-world networks, such as those representing metabolic and protein-protein interaction networks as well as the interaction between secondary structure elements in proteins.