Modeling the Concentric Organization of Lattices and Path-Regular Networks

Abstract

"The concentric organization of a complex network with respect to a reference node can provide rich information about both the topology and the dynamics of complex networks. Particularly, measurements such as the hierarchical number of nodes, the hierarchical degree and the intra-ring degree have been recently shown (arXiv:0802.0421 and arXiv:0802.1272) to define important features of non-linear dynamics taking place in complex networks. The current article reports theoretical models capable of reproducing with high accuracy the concentric organization, expressed in terms of the three just-mentioned measurements, of two important types of networks, namely orthogonal lattices and path-regular structures. The potential of such models is illustrated with respect to their application to systematic characterization of non-linear dynamics in those two types of networks, more specifically the prediction of avalanches of spikes and their properties. While the considered orthogonal lattices were found not to exhibit avalanches, the path-regular networks imply avalanches depending of their parametric configurations."