Universal scaling of distances in complex networks

Prelegent(ci)

Janusz A. Hołyst

Afiliacja

Faculty of Physics, Center of Excellence for Complex Systems Research, Warsaw University of Technology

Termin

25 kwietnia 2007 16:15

Pokój

p. 5840

Seminarium

Seminarium Zakładu Biomatematyki i Teorii Gier

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Universal scaling of distances between vertices of Erdos-Renyi random graphs, scale-free Barabasi-Albert models, science collaboration networks, biological networks, Internet Autonomous Systems and public transport networks are observed. A mean distance distance between two nodes of degrees k_i and k_j equals to = A - B log(k_i*k_j ). The scaling is valid over several decades. A simple theory for the appearance of this scaling is presented. Parameters A and B depend on the mean value of a node degree _nn calculated for the nearest neighbors, on network clustering coefficients and degree-degree correlations. We can also explain log- periodic oscillations around this law by the discrete character of inter-node distances. References 1. Janusz A. Ho�yst, Julian Sienkiewicz, Agata Fronczak, Piotr Fronczak and Krzysztof Suchecki, Universal scaling of distances in complex networks, Phys. Rev. E 72,026108 (2005) 2. Julian Sienkiewicz, Piotr Fronczak, Janusz A. Holyst, Log-periodic oscillations due to discrete effects in complex networks, arXiv:cond-mat/0608273, Phys. Rev. E inprint, 2007.

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