Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modeling Social Networks with Overlapping Communities Using Hypergraphs
  and Their Line Graphs   We propose that hypergraphs can be used to model social networks with
overlapping communities. The nodes of the hypergraphs represent the
communities. The hyperlinks of the hypergraphs denote the individuals who may
participate in multiple communities. The hypergraphs are not easy to analyze,
however, the line graphs of hypergraphs are simple graphs or weighted graphs,
so that the network theory can be applied. We define the overlapping depth $k$
of an individual by the number of communities that overlap in that individual,
and we prove that the minimum adjacency eigenvalue of the corresponding line
graph is not smaller than $-k_{max}$, which is the maximum overlapping depth of
the whole network. Based on hypergraphs with preferential attachment, we
establish a network model which incorporates overlapping communities with
tunable overlapping parameters $k$ and $w$. By comparing with the Hyves social
network, we show that our social network model possesses high clustering,
assortative mixing, power-law degree distribution and short average path
length.

10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
18
The categories of this paper are: econ