A generalized approach to complex networks
Institute of Physics of São Carlos, University of São Paulo, Caixa Postal: 369, CEP:, 13560-970 São Carlos, SP, Brazil
Revised: 23 November 2005
Published online: 12 April 2006
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the network topology to new network growth models. First, the concepts of node degree and clustering coefficient are extended in order to characterize not only specific nodes, but any generic subnetwork. Second, the consideration of distance transform and rings are used to further extend those concepts in order to obtain a signature, instead of a single scalar measurement, ranging from the single node to whole graph scales. The enhanced discriminative potential of such extended measurements is illustrated with respect to the identification of correspondence between nodes in two complex networks, namely a protein-protein interaction network and a perturbed version of it.
PACS: 02.70.Rr – General statistical methods / 02.10.Ox – Combinatorics; graph theory / 89.75.Hc – Networks and genealogical trees
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006