title: Thermodynamic characterization of synchronization-optimized oscillator networks.
abstract: We consider a canonical ensemble of synchronization-optimized networks of identical oscillators under external noise. By performing a Markov chain Monte Carlo simulation using the Kirchhoff index, i.e., the sum of the inverse eigenvalues of the Laplacian matrix (as a graph Hamiltonian of the network), we construct more than 1,000 different synchronization-optimized networks. We then show that the transition from star to core-periphery structure depends on the connectivity of the network, and is characterized by the node degree variance of the synchronization-optimized ensemble. We find that thermodynamic properties such as heat capacity show anomalies for sparse networks.
authors.affiliation: Department of Engineering Science, Osaka Electro-Communication University, Neyagawa 572-8530, Japan.
authors.forename: Tatsuo
authors.initials: T
authors.lastname: Yanagita
authors.affiliation: Department of Biomedical Informatics, Gifu University School of Medicine, 1-1 Yanagido, Gifu, Gifu 501-1194, Japan.
authors.forename: Takashi
authors.initials: T
authors.lastname: Ichinomiya