Transitive closure and metric inequality of weighted graphs: detecting protein interaction modules using cliques

Authors:
Chris Ding;Xiaofeng He;Hui Xiong;Hanchuan Peng;Stephen R. Holbrook
Affiliations:
Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA.;Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA.;Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA.;Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA.;Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA
Venue:
International Journal of Data Mining and Bioinformatics
Year:
2006

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Abstract

We study transitivity properties of edge weights in complex networks. We show that enforcing transitivity leads to a transitivity inequality which is equivalent to ultra-metric inequality. This can be used to define transitive closure on weighted undirected graphs, which can be computed using a modified Floyd-Warshall algorithm. These new concepts are extended to dissimilarity graphs and triangle inequalities. From this, we extend the clique concept from unweighted graph to weighted graph. We outline several applications and present results of detecting protein functional modules in a protein interaction network.