Small subgraph counts can be used as summary statistics for large random graphs. We use the Stein–Chen method to derive Poisson approximations for the distribution of the number of subgraphs in the stochastic block model which are isomorphic to some fixed graph. We also obtain Poisson approximations for subgraph counts in a graphon-type generalisation of the model in which the edge probabilities are (possibly dependent) random variables supported on a subset of . Our results apply when the fixed graph is a member of the class of strictly balanced graphs.
Accepté le :
DOI : 10.1051/ps/2016006
Mots clés : Graphon model, stochastic block model, Erdős–Rényi Mixture Model, subgraph counts, Poisson approximation, Stein–Chen method
@article{PS_2016__20__131_0,
author = {Coulson, Matthew and Gaunt, Robert E. and Reinert, Gesine},
title = {Poisson approximation of subgraph counts in stochastic block models and a graphon model},
journal = {ESAIM: Probability and Statistics},
pages = {131--142},
publisher = {EDP-Sciences},
volume = {20},
year = {2016},
doi = {10.1051/ps/2016006},
mrnumber = {3528620},
zbl = {1353.05112},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2016006/}
}
TY - JOUR AU - Coulson, Matthew AU - Gaunt, Robert E. AU - Reinert, Gesine TI - Poisson approximation of subgraph counts in stochastic block models and a graphon model JO - ESAIM: Probability and Statistics PY - 2016 SP - 131 EP - 142 VL - 20 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2016006/ DO - 10.1051/ps/2016006 LA - en ID - PS_2016__20__131_0 ER -
%0 Journal Article %A Coulson, Matthew %A Gaunt, Robert E. %A Reinert, Gesine %T Poisson approximation of subgraph counts in stochastic block models and a graphon model %J ESAIM: Probability and Statistics %D 2016 %P 131-142 %V 20 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2016006/ %R 10.1051/ps/2016006 %G en %F PS_2016__20__131_0
Coulson, Matthew; Gaunt, Robert E.; Reinert, Gesine. Poisson approximation of subgraph counts in stochastic block models and a graphon model. ESAIM: Probability and Statistics, Tome 20 (2016), pp. 131-142. doi : 10.1051/ps/2016006. http://www.numdam.org/articles/10.1051/ps/2016006/
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