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Dresden 2017 – scientific programme

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BP: Fachverband Biologische Physik

BP 50: Networks: From Topology to Dynamics I (Joint Session SOE/DY/BP)

BP 50.2: Talk

Thursday, March 23, 2017, 10:00–10:15, GÖR 226

Large-deviation properties of the stochastic block model — •Stephan Adolf1, Tiago P. Peixoto2, and Alexander K. Hartmann11Institut of Physics, University of Oldenburg — 2Department of Mathematical Sciences, University of Bath

In this contribution we study the distribution of the size of the largest components for the stochastic block model. The stochastic block model is a generative model for graphs, which can be used to model social relationships [1, 2]. Suppose NN vertices which can partioned into at least two groups (also called blocks). For generating a graph in the stochastic block model ensemble one inserts edges between pairs of vertices with different probabilities depending on whether the vertices are in the same group or not [1]. To obtain the distribution of the size of the largest component over the full support we use a large-deviation method [3] to determine even small probabilities (like for example 10−100). We compare the results to those obtained for Erdős-Rhényi random graphs.

[1] A. Decelle and F. Krzakala and C. Moore and L. Zdeborová, Phys. Rev. E 84, 066106 (2011)

[2] P.W. Holland and K.B. Laskey and S. Leinhardt, Social networks 5, 109-137 (1983)

[3] A.K. Hartmann, Eur. Phys. J. B 84, 627-634 (2011)

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