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Percolation of spatially constrained Erdos-R enyi networks with degree correlations
Schmeltzer, C.; Soriano i Fradera, Jordi; Sokolov, Igor M., 1958-; Rüdiger, S.
Universitat de Barcelona
Motivated by experiments on activity in neuronal cultures [J. Soriano, M. Rodr ́ıguez Mart́ınez, T. Tlusty, and E. Moses, Proc. Natl. Acad. Sci. 105, 13758 (2008)], we investigate the percolation transition and critical exponents of spatially embedded Erd̋os-Ŕenyi networks with degree correlations. In our model networks, nodes are randomly distributed in a two-dimensional spatial domain, and the connection probability depends on Euclidian link length by a power law as well as on the degrees of linked nodes. Generally, spatial constraints lead to higher percolation thresholds in the sense that more links are needed to achieve global connectivity. However, degree correlations favor or do not favor percolation depending on the connectivity rules. We employ two construction methods to introduce degree correlations. In the first one, nodes stay homogeneously distributed and are connected via a distance- and degree-dependent probability. We observe that assortativity in the resulting network leads to a decrease of the percolation threshold. In the second construction methods, nodes are first spatially segregated depending on their degree and afterwards connected with a distance-dependent probability. In this segregated model, we find a threshold increase that accompanies the rising assortativity. Additionally, when the network is constructed in a disassortative way, we observe that this property has little effect on the percolation transition.
Percolació (Física estadística)
Neurociències
Topologia
Dinàmica
Xarxes socials
Xarxes neuronals (Neurobiologia)
Percolation (Statistical physics)
Neurosciences
Topology
Dynamics
Social networks
Neural networks (Neurobiology)
(c) American Physical Society, 2014
Article
info:eu-repo/semantics/publishedVersion
American Physical Society
         

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