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

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

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)162-177
Number of pages16
JournalInternational Journal of Data Mining and Bioinformatics
Volume1
Issue number2
DOIs
StatePublished - 2006
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Biochemistry, Genetics and Molecular Biology(all)
  • Library and Information Sciences

Keywords

  • protein interaction
  • transitive closure
  • triangle inequality
  • ultrametric
  • weighted graph

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