Uncovering structure in biological networks

The Erd̈os-Ŕenyi model of a network is simple and possesses many explicit expressions for average and asymptotic properties, but it d oes not fit well to real-word networks. The vertices of these networks are often structur ed in prior unknown clusters (functionally related proteins or social communities) wit h different connectivity properties. We define a generalisation of the Erd ös-Ŕenyi model called ERMG for Erd ös-Ŕenyi Mixtures for Graphs. This new model is based on mixture distr ibutions. We give some of its properties, an algorithm to estimate its parameters and pply this method to uncover the modular structure of a network of enzymatic reactions.

[1]  S. L. Wong,et al.  Motifs, themes and thematic maps of an integrated Saccharomyces cerevisiae interaction network , 2005, Journal of biology.

[2]  Masanori Arita.  The metabolic world of Escherichia coli is not small. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[3]  M. Newman.  Fast algorithm for detecting community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  S. Shen-Orr,et al.  Network motifs in the transcriptional regulation network of Escherichia coli , 2002, Nature Genetics.

[5]  S H Strogatz,et al.  Random graph models of social networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[6]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[7]  Gérard Govaert,et al.  Assessing a Mixture Model for Clustering with the Integrated Completed Likelihood , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  Bruce A. Reed,et al.  A Critical Point for Random Graphs with a Given Degree Sequence , 1995, Random Struct. Algorithms.

[9]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[10]  A. Andrew,et al.  Emergence of Scaling in Random Networks , 1999 .