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Discovering bipartite substructure in directed networks

Part of: Discrete mathematics in relation to computer science Mathematical biology in general

Published online by Cambridge University Press:  01 February 2011

Alan Taylor ,
J. Keith Vass  and
Desmond J. Higham
Alan Taylor
Affiliation:
Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XH, United Kingdom (email: [email protected])
J. Keith Vass
Affiliation:
Translational Medical Research Collaboration, The Sir James Black Centre, University of Dundee, Dundee, DD1 5EH, United Kingdom (email: [email protected])
Desmond J. Higham
Affiliation:
Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XH, United Kingdom (email: [email protected])

Abstract

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Bipartivity is an important network concept that can be applied to nodes, edges and communities. Here we focus on directed networks and look for subnetworks made up of two distinct groups of nodes, connected by ‘one-way’ links. We show that a spectral approach can be used to find hidden substructures of this form. Theoretical support is given for the idealized case where there is limited overlap between subnetworks. Numerical experiments show that the approach is robust to spurious and missing edges. A key application of this work is in the analysis of high-throughput gene expression data, and we give an example where a biologically meaningful directed bipartite subnetwork is found from a cancer microarray dataset.

MSC classification

Secondary: 68R10: Graph theory (including graph drawing) 92B05: General biology and biomathematics
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 14 , 2011 , pp. 72 - 86
Copyright
Copyright © London Mathematical Society 2011

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