Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniqueness of communities in regular stochastic block models   This paper studies the regular stochastic block model comprising
\emph{several} communities: each of the $k$ non-overlapping communities, for $k
\geqslant 3$, possesses $n$ vertices, each of which has total degree $d$. The
values of the intra-cluster degrees (i.e.\ the number of neighbours of a vertex
inside the cluster it belongs to) and the inter-cluster degrees (i.e.\ the
number of neighbours of a vertex inside a cluster different from its own) are
allowed to vary across clusters. We discuss two main results: the first
compares the probability measure induced by our model with the uniform measure
on the space of $d$-regular graphs on $kn$ vertices, and the second establishes
that the clusters, under rather weak assumptions, are unique asymptotically
almost surely as $n \rightarrow \infty$.

23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
19
The categories of this paper are: eess
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th