Int. J. of Data Mining and Bioinformatics   »   2006 Vol.1, No.2

 

 

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

 

Author: Chris Ding, Xiaofeng He, Hui Xiong, Hanchuan Peng, Stephen R. Holbrook

 

Addresses:
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

 

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.

 

Keywords: transitive closure; ultrametrics; triangle inequality; weighted graphs; protein interaction; bioinformatics; edge weights; clique; complex networks; network transitivity.

 

DOI: 10.1504/IJDMB.2006.010854

 

Int. J. of Data Mining and Bioinformatics, 2006 Vol.1, No.2, pp.162 - 177

 

Available online: 07 Sep 2006

 

 

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