Thermodynamic Analysis of Time Evolving Networks

Abstract

The problem of how to represent networks, and from this representation, derive succinct characterizations of network structure and in particular how this structure evolves with time, is of central importance in complex network analysis. This paper tackles the problem by proposing a thermodynamic framework to represent the structure of time-varying complex networks. More importantly, such a framework provides a powerful tool for better understanding the network time evolution. Specifically, the method uses a recently-developed approximation of the network von Neumann entropy and interprets it as the thermodynamic entropy for networks. With an appropriately-defined internal energy in hand, the temperature between networks at consecutive time points can be readily derived, which is computed as the ratio of change of entropy and change in energy. It is critical to emphasize that one of the main advantages of the proposed method is that all these thermodynamic variables can be computed in terms of simple network statistics, such as network size and degree statistics. To demonstrate the usefulness of the thermodynamic framework, the paper uses real-world network data, which are extracted from time-evolving complex systems in the financial and biological domains. The experimental results successfully illustrate that critical events, including abrupt changes and distinct periods in the evolution of complex networks, can be effectively characterized.