Statistical-mechanical approach to subgraph centrality in complex networks

• DOI: 10.1016/j.cplett.2007.03.098
• Publication Date: 2007-03-31T11:19:02Z
• Authors: Ernesto Estrada; Naomichi Hatano
• Keywords: Physics - Physics and Society; Statistical Mechanics (cond-mat.stat-mech); FOS: Physical sciences; Physics and Society (physics.soc-ph); 0101 mathematics; 01 natural sciences; Condensed Matter - Statistical Mechanics

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.<br/>17 pages, 2 figures<br/>