Graph Entropy from Closed Walk and Cycle Functionals

Aziz, Furqan; Hancock, Edwin R.; Wilson, Richard C.

doi:10.1007/978-3-319-49055-7_16

Cited by 3 publications

(3 citation statements)

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“…This index has found multiple applications in the study of protein function [16]. In a related work [2], we have used frequencies of closed walks and cycles to estimate the entropy of a graph.…”

Section: Related Literaturementioning

confidence: 99%

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Network entropy using edge-based information functionals

Aziz

Hancock

Wilson

2020

Journal of Complex Networks

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In this article, we present a novel approach to analyse the structure of complex networks represented by a quantum graph. A quantum graph is a metric graph with a differential operator (including the edge-based Laplacian) acting on functions defined on the edges of the graph. Every edge of the graph has a length interval assigned to it. The structural information contents are measured using graph entropy which has been proved useful to analyse and compare the structure of complex networks. Our definition of graph entropy is based on local edge functionals. These edge functionals are obtained by a diffusion process defined using the edge-based Laplacian of the graph using the quantum graph representation. We first present the general framework to define graph entropy using heat diffusion process and discuss some of its properties for different types of network models. Second, we propose a novel signature to gauge the structural complexity of the network and apply the proposed method to different datasets.

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Section: Related Literaturementioning

confidence: 99%

“…Tox 21 [29]: These graphs are derived from the data published by the National Center for Advancing Translational Sciences in the context of the Tox21 Data Challenge 2014 2 . These datasets each contain more than 7000 graphs and the goal here is to asses the performance of the proposed method on larger datasets.…”

Section: Functional Brain Network Analysis Datamentioning

confidence: 99%

Network entropy using edge-based information functionals

Aziz

Hancock

Wilson

2020

Journal of Complex Networks

Self Cite

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“…Cao et al (19) have defined graph entropies based on independent sets and matching of graphs. Recently Aziz et al (20) have presented an information functional that is defined using closed random walks and cycle functionals. They have applied their method to timeseries networks and have shown that the obtained measures is more accurate in comparing graphs when compared to alternate information functionals defined in (18).…”

Section: Introductionmentioning

confidence: 99%