Publications Mathématiques de Besançon
Algèbre et Théorie des Nombres
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Nicolas Wicker; Canh Hao Nguyen; Hiroshi Mamitsuka
Some properties of a dissimilarity measure for labeled graphs
Publications mathématiques de Besançon (2016), p. 85-94
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Class. Math.: 05C50, 15A18
Keywords: Labeled graphs, Graph spectrum, Dissimilarity, Bridge effect.

Abstract

We investigate the problem of comparing different graphs on the same set of vertices. It is a problem arising when using different biological networks to elucidate cellular processes. We wish to see their similarity and difference via connectivity-aware graph dissimilarity for graphs with the same node set. We extend a previous result and present some results concerning the orders of magnitude of the dissimilarity as the graphs’ sizes grow to infinity. We find that removing an edge playing a very important role in graph connectivity, such as a bridge between two fully connected subgraphs, can have a dramatic effect on the dissimilarity compared to the removal of any “ordinary” edge.

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