title: Transitive closure and metric inequality of weighted graphs: detecting protein interaction modules using cliques.
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.
authors.affiliation: Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA. chqding@lbl.gov
authors.forename: Chris
authors.initials: C
authors.lastname: Ding
authors.forename: Xiaofeng
authors.initials: X
authors.lastname: He
authors.forename: Hui
authors.initials: H
authors.lastname: Xiong
authors.forename: Hanchuan
authors.initials: H
authors.lastname: Peng
authors.forename: Stephen R
authors.initials: SR
authors.lastname: Holbrook
mesh_terms: D000465:Algorithms; D019295:Computational Biology; D005656:Fungal Proteins / Q000378:metabolism; D008962:Models, Theoretical; D011485:Protein Binding; D025941:Protein Interaction Mapping / Q000379:methods*; D049490:Systems Biology
chemical_list: D005656:Fungal Proteins