Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compound Poisson approximation of subgraph counts in stochastic block
  models with multiple edges   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. Both the cases that the fixed graph is a simple graph and
that it has multiple edges are treated. 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 \cite{kn11}.

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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph