Some properties of a dissimilarity measure for labeled graphs
Publications Mathématiques de Besançon (2016), pp. 85-94.

Nous nous intéressons au problème de la comparaison de graphes sur un même ensemble de sommets. C’est un problème apparaissant dans l’étude de réseaux biologiques lorsqu’on veut comprendre le fonctionnement de processus cellulaires. L’objectif est de lier leur similarité ou différence, par une mesure consciente de la connectivité du graphe sur un même ensemble de sommets. Nous étendons un résultat antérieur et présentons de nouveaux résultats sur l’ordre de grandeur de la dissimilarité lorsque la taille des graphes tend vers l’infini. En particulier, nous montrons que la suppression d’une arête qui joue une grande importance dans la connectivité d’un graphe, comme un pont, peut avoir un effet dramatique sur la dissimilarité par rapport à la suppression d’une arête « ordinaire ».

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.

Reçu le : 2015-04-11
Publié le : 2016-12-13
DOI : https://doi.org/10.5802/pmb.o-7
Classification : 05C50,  15A18
Mots clés: Labeled graphs, Graph spectrum, Dissimilarity, Bridge effect.
@article{PMB_2016____85_0,
     author = {Nicolas Wicker and Canh Hao Nguyen and Hiroshi Mamitsuka},
     title = {Some properties of a dissimilarity measure for labeled graphs},
     journal = {Publications Math\'ematiques de Besan\c con},
     pages = {85--94},
     publisher = {Presses universitaires de Franche-Comt\'e},
     year = {2016},
     doi = {10.5802/pmb.o-7},
     zbl = {1408.05085},
     language = {en},
     url = {pmb.centre-mersenne.org/item/PMB_2016____85_0/}
}
Nicolas Wicker; Canh Hao Nguyen; Hiroshi Mamitsuka. Some properties of a dissimilarity measure for labeled graphs. Publications Mathématiques de Besançon (2016), pp. 85-94. doi : 10.5802/pmb.o-7. https://pmb.centre-mersenne.org/item/PMB_2016____85_0/

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