Network edge entropy from maxwell-boltzmann statistics

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

*Corresponding author for this work

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

3 Citations (Scopus)


In prior work, we have shown how to compute global network entropy using a heat bath analogy and Maxwell-Boltzmann statistics. In this work, we show how to project out edge-entropy components so that the detailed distribution of entropy across the edges of a network can be computed. This is particularly useful if the analysis of non-homogeneous networks with a strong community as hub structure is being attempted. To commence, we view the normalized Laplacian matrix as the network Hamiltonian operator which specifies a set of energy states with the Laplacian eigenvalues. The network is assumed to be in thermodynamic equilibrium with a heat bath. According to this heat bath analogy, particles can populate the energy levels according to the classical Maxwell-Boltzmann distribution, and this distribution together with the energy states determines thermodynamic variables of the network such as entropy and average energy. We show how the entropy can be decomposed into components arising from individual edges using the eigenvectors of the normalized Laplacian. Compared to previous work based on the von Neumann entropy, this thermodynamic analysis is more effective in characterizing changes of network structure since it better represents the edge entropy variance associated with edges connecting nodes of large degree. Numerical experiments on real-world datasets are presented to evaluate the qualitative and quantitative differences in performance.

Original languageEnglish
Title of host publicationImage Analysis and Processing - ICIAP 2017 - 19th International Conference, Proceedings
EditorsRaimondo Schettini, Sebastiano Battiato, Giovanni Gallo, Filippo Stanco
PublisherSpringer Verlag
Number of pages11
ISBN (Print)9783319685595
Publication statusPublished - 2017
Externally publishedYes
Event19th International Conference on Image Analysis and Processing, ICIAP 2017 - Catania, Italy
Duration: 11 Sept 201715 Sept 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10484 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference19th International Conference on Image Analysis and Processing, ICIAP 2017


  • Maxwell-Boltzmann statistics
  • Network edge entropy


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