Modeling the concentric organization of lattices and path-regular networks and Its Application to Complex Neuronal Networks Analysis

Luciano da Fontoura Costa (1)

1 IFSC - IFSC-USP

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 integrate-and-fire dynamics in those two types of networks, more specifically the prediction of avalanches of spikes and their properties. (Copyright L. da F. Costa, 21st Feb 2008).

Mots clés: complex networks; neuronal networks; complex systems; computational physics

Domaines: Physique Numérique [physics.comp-ph]

Luciano da Fontoura Costa. Modeling the concentric organization of lattices and path-regular networks and Its Application to Complex Neuronal Networks Analysis. 2008. ⟨hal-00258893v2⟩