Berlin 2012 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 18: Networks II (with SOE)

DY 18.2: Talk

Wednesday, March 28, 2012, 10:30–10:45, H 0110

Topological properties of networks with spatial constraints — •Stefano Mattiello¹, Shlomo Havlin², and Armin Bunde¹ — ¹Institut für Theoretische Physik, Justus-Liebig-Universität Giessen, Giessen, Germany — ²Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan, Israel

We investigate the effects of spatial constraints on the topological properties of networks embedded in one or two dimensional space. The nodes are embedded in a linear chain or in a square lattice with embedding dimension d_e=1 and d_e=2, respectively. The length of the links are chosen with probability p(r) ∼ r^−δ , where r is the Euclidean distance between them. We consider Erdös -Rényi networks, where the distribution of the degrees of the nodes is Poissonian, as well as scale-free networks where the degree distribution follows a power law P(k)∼ k ^−γ , with γ typically between two and three.

We study the mean topological distance l and the clustering coefficient C of both kind of networks. We focus on the dependence of these properties on the size of the system N and the exponent δ, in particular in the region d_e≤δ≤ 2d_e, where we expect an anomalous behavior.