Explore Statistical Properties of Undirected Unweighted Networks from Ensemble Models

Complex network theory has been widely demonstrated as a powerful tool in modeling and characterizing various complex systems. In the past, complex network theory has focused on the behaviors as well as the characteristics of the network nodes and edges. However, with the continuous evolution of society, traditional graph theory faces challenges due to the emergence of extermely large network structures. Recently, complex network method based statistics has attracted much attention. The new approach effectively manages very large networks and uncovers their intrinsic properties. In this paper, we present a complex network analysis model for undirected, unweighted networks based on a statistical analysis approach. This model is inspired by the ensemble model in thermostatistical physics. Based on the established mathematical model, we derive physical measures that reflect the intrinsic properties of the network, including Entropy, Free Energy, Temperature, and so on. In the experimental part, we first explored the mathematical characterization of these metrics. Then, we observed the performance of various network categories under the same metric. Finally, we applied these measures to the field of graph classification. Extensive experiments demonstrate the effectiveness and superiority of the proposed method.