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Thermodynamic Analysis of Time Evolving Networks

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JournalEntropy
DateAccepted/In press - 28 Sep 2018
Number of pages15
Original languageEnglish

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 to 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.

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