Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discovering Nested Communities   Finding communities in graphs is one of the most well-studied problems in
data mining and social-network analysis. In many real applications, the
underlying graph does not have a clear community structure. In those cases,
selecting a single community turns out to be a fairly ill-posed problem, as the
optimization criterion has to make a difficult choice between selecting a tight
but small community or a more inclusive but sparser community.
  In order to avoid the problem of selecting only a single community we propose
discovering a sequence of nested communities. More formally, given a graph and
a starting set, our goal is to discover a sequence of communities all
containing the starting set, and each community forming a denser subgraph than
the next. Discovering an optimal sequence of communities is a complex
optimization problem, and hence we divide it into two subproblems: 1) discover
the optimal sequence for a fixed order of graph vertices, a subproblem that we
can solve efficiently, and 2) find a good order. We employ a simple heuristic
for discovering an order and we provide empirical and theoretical evidence that
our order is good.

16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph