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Discovering bipartite substructure in directed networks

  • Alan Taylor (a1), J. Keith Vass (a2) and Desmond J. Higham (a3)

Abstract

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.

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References

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[1]Barash, D., ‘Second eigenvalue of the Laplacian matrix for predicting RNA conformational switch by mutation’, Bioinformatics 20 (2004) 18611869.
[2]de Silva, E. and Stumpf, M. P. H., ‘Complex networks and simple models in biology’, J. R. Soc. Interface 2 (2005) 419430.
[3]Estrada, E., ‘Protein bipartivity and essentiality in the yeast protein–protein interaction network’, J. Proteome Res. 5 (2006) 21772184.
[4]Estrada, E. and Hatano, N., ‘Communicability in complex networks’, Phys. Rev. E 77 (2008) 036111.
[5]Estrada, E., Higham, D. J. and Hatano, N., ‘Communicability and multipartite structures in complex networks at negative absolute temperatures’, Phys. Rev. E 78 (2008) 026102.
[6]Estrada, E. and Rodríguez-Velázquez, J., ‘Spectral measures of bipartivity in complex networks’, Phys. Rev. E 72 (2005) 046105.
[7]Golub, G. H. and Van Loan, C. F., Matrix computations, 3rd edn (Johns Hopkins University Press, Baltimore, 1996).
[8]Grindrod, P. and Kibble, M., ‘Review of uses of network and graph theory concepts within proteomics’, Expert Rev. Proteom. 1 (2004) 229238.
[9]Holme, P., Liljeros, F., Edling, C. R. and Kim, B. J., ‘Network bipartivity’, Phys. Rev. E 68 (2003) 056107.
[10]Hu, Y. and Scott, J. A., HSL_MC73: a fast multilevel Fiedler and profile reduction code, RAL-TR-2003-36, Numerical Analysis Group, Computational Science and Engineering Department, Rutherford Appleton Laboratory, 2003.
[11]Morrison, J. L., Breitling, R., Higham, D. J. and Gilbert, D. R., ‘A lock-and-key model for protein–protein interactions’, Bioinformatics 2 (2006) 20122019.
[12]Spence, A., Stoyanov, Z. and Vass, J. K., ‘The sensitivity of spectral clustering applied to gene expression data’, Proceedings of the 1st International Conference on Bioinformatics and Biomedical Engineering, 2007, 1343–1346.
[13]Taylor, A. J., ‘Computational tools for complex networks’, PhD Thesis, University of Strathclyde, 2009.
[14]Thomas, A., Cannings, R., Monk, N. A. M. and Cannings, C., ‘On the structure of protein–protein interaction networks’, Biochem. Soc. Trans. 31 (2003) 14911496.
[15]Valk, P. J., Verhaak, R. G., Beijen, M. A., Erpelinck, C. A., van Waalwijk van Doorn-Khosrovani, S. B., Boer, J. M., Beverloo, H. B., Moorhouse, M. J., van der Spek, P. J., Lüwenberg, B. and Delwel, R., ‘Prognostically useful gene-expression profiles in acute myeloid leukemia’, New Engl. J. Med. 16 (2004) 16171628.
[16]Vass, J. K., Higham, D. J., Mao, X. and Crowther, D., ‘New controls of TCA-cycle genes revealed in networks built by discretization or correlation’, Technical Report, Department of Mathematics, University of Strathclyde, Glasgow, UK, 2009, 10.
[17]Walshaw, C. and Cross, M., ‘JOSTLE: parallel multilevel graph-partitioning software – an overview’, Mesh partitioning techniques and domain decomposition techniques (ed. Magoules, F.; Saxe-Coburg Publications, Stirling, UK, 2007) 2758.
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LMS Journal of Computation and Mathematics
  • ISSN: -
  • EISSN: 1461-1570
  • URL: /core/journals/lms-journal-of-computation-and-mathematics
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