Network entropy analysis using the Maxwell-Boltzmann partition function

Jianjia Wang, Richard C. Wilson, Edwin R. Hancock

Research output: Chapter in Book or Report/Conference proceedingConference Proceedingpeer-review

12 Citations (Scopus)


In this paper, we use the Maxwell-Boltzmann partition function to compute network entropy. The partition function is used to model the energy level population statistics where the network is in thermodynamic equilibrium with a heat-bath. Here the network Hamiltonian operator defines a set of energy levels occupied by particles in thermal equilibrium. These energy levels are given by the eigenvalues of the normalized Laplacian matrix. In other words, we investigate a thermalised version of the system normally studied in spectral graph theory, where the thermalisation accounts for noise in the system. We provide a systematic study of the entropy resulting from this characterization. Compared to previous work based on using von Neumann network entropy, this thermodynamic quantity is effective in characterizing changes of network structure and distinguishing different types of network models (e.g. Erdos-Rényi random graphs, small world networks, and scale free networks). Numerical experiments on real world data-sets are presented to evaluate the qualitative and quantitative differences in performance.

Original languageEnglish
Title of host publication2016 23rd International Conference on Pattern Recognition, ICPR 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781509048472
Publication statusPublished - 1 Jan 2016
Externally publishedYes
Event23rd International Conference on Pattern Recognition, ICPR 2016 - Cancun, Mexico
Duration: 4 Dec 20168 Dec 2016

Publication series

NameProceedings - International Conference on Pattern Recognition
ISSN (Print)1051-4651


Conference23rd International Conference on Pattern Recognition, ICPR 2016


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