| Issue |
ESAIM: PS
Volume 20, 2016
|
|
|---|---|---|
| Page(s) | 131 - 142 | |
| DOI | https://doi.org/10.1051/ps/2016006 | |
| Published online | 14 July 2016 | |
Poisson approximation of subgraph counts in stochastic block models and a graphon model
1 The Queen’s College, University of Oxford, High Street,
Oxford, OX1 4AW, UK.
matthew.coulson@queens.ox.ac.uk
2 Department of Statistics, University of Oxford, 24-29 St
Giles’, Oxford OX1 3LB, UK.
gaunt@stats.ox.ac.uk; reinert@stats.ox.ac.uk
Received:
8
October
2015
Revised:
22
February
2016
Accepted:
2
March
2016
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 [ 0,1 ]. Our results apply when the fixed graph is a member of the class of strictly balanced graphs.
Mathematics Subject Classification: 90B15 / 62E17 / 60F05 / 05C80
Key words: Graphon model / stochastic block model / Erdős–Rényi Mixture Model / subgraph counts / Poisson approximation / Stein–Chen method
© EDP Sciences, SMAI 2016
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