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Compound Poisson approximation of subgraph counts in stochastic block models with multiple edges
| Content Provider | Scilit |
|---|---|
| Author | Coulson, Matthew Gaunt, Robert E. Reinert, Gesine |
| Copyright Year | 2018 |
| Description | We use the Stein‒Chen method to obtain compound Poisson approximations for the distribution of the number of subgraphs in a generalised stochastic block model which are isomorphic to some fixed graph. This model generalises the classical stochastic block model to allow for the possibility of multiple edges between vertices. We treat the case that the fixed graph is a simple graph and that it has multiple edges. The former results apply when the fixed graph is a member of the class of strictly balanced graphs and the latter results apply to a suitable generalisation of this class to graphs with multiple edges. We also consider a further generalisation of the model to pseudo-graphs, which may include self-loops as well as multiple edges, and establish a parameter regime in the multiple edge stochastic block model in which Poisson approximations are valid. The results are applied to obtain Poisson and compound Poisson approximations (in different regimes) for subgraph counts in the Poisson stochastic block model and degree corrected stochastic block model of Karrer and Newman (2011). |
| Related Links | http://arxiv.org/pdf/1710.06341 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A97FB752EE26DF710DDC6404732D3FFC/S0001867818000356a.pdf/div-class-title-compound-poisson-approximation-of-subgraph-counts-in-stochastic-block-models-with-multiple-edges-div.pdf |
| Ending Page | 782 |
| Page Count | 24 |
| Starting Page | 759 |
| ISSN | 00018678 |
| e-ISSN | 14756064 |
| DOI | 10.1017/apr.2018.35 |
| Journal | Advances in Applied Probability |
| Issue Number | 3 |
| Volume Number | 50 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2018-09-01 |
| Access Restriction | Open |
| Subject Keyword | Advances in Applied Probability Interdisciplinary Mathematics Statistics and Probability Stochastic Block Model Compound Poisson Approximation Stein‒chen Method |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Statistics and Probability |
