Thermodynamic Analysis of Time Evolving Networks


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.

Publication DOI:
Divisions: College of Engineering & Physical Sciences
?? 50811700Jl ??
College of Engineering & Physical Sciences > Systems analytics research institute (SARI)
Additional Information: © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (
Publication ISSN: 1099-4300
Last Modified: 25 Apr 2024 07:13
Date Deposited: 10 Oct 2018 08:04
Full Text Link:
Related URLs: http://www.mdpi ... -4300/20/10/759 (Publisher URL)
PURE Output Type: Article
Published Date: 2018-10-02
Accepted Date: 2018-09-28
Authors: Ye, Cheng
Wilson, Richard
Rossi, Luca (ORCID Profile 0000-0002-6116-9761)
Torsello, Andrea
Hancock, Edwin



Version: Published Version

License: Creative Commons Attribution

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