Dresden 2017 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe
BP: Fachverband Biologische Physik
BP 50: Networks: From Topology to Dynamics I (Joint Session SOE/DY/BP)
BP 50.2: Vortrag
Donnerstag, 23. März 2017, 10:00–10:15, GÖR 226
Large-deviation properties of the stochastic block model — •Stephan Adolf1, Tiago P. Peixoto2, and Alexander K. Hartmann1 — 1Institut 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 N ∈ N 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)