On Motif Statistics in Symmetric Networks

Blake Stacey
Ecole Normale Superieure de Lyon

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     Last modified: August 16, 2006

Abstract
In recent years, networks derived from complex systems have been
studied not just in terms of global properties like degree
distributions, but also in terms of motifs, small subgraphs whose
appearances can be examined statistically. Motifs which occur more
often than chance predicts are often presumed to indicate some feature
of local structure which is preferred for biological, physical or
geometrical reasons. I test a claim made in R. Milo et al., Science 303
(5 March 2004) to the effect that protein structures can be approached
in this way, studying not three proteins but a set of 830. Overall, the
general claim of the earlier paper is borne out: the spatial
distribution of secondary-structure elements can be roughly understood
as a geometrically constrained network. Structures of individual
proteins are reflected in the clustering coefficients of the networks
derived from the protein geometries. The nature of geometrical
constraints on network topology raises issues of symmetry, which also
affect the ways the presence of multiple protein domains can skew motif
statistics.