Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Community Structures Are Definable in Networks: A Structural Theory of
  Networks   We found that neither randomness in the ER model nor the preferential
attachment in the PA model is the mechanism of community structures of
networks, that community structures are universal in real networks, that
community structures are definable in networks, that communities are
interpretable in networks, and that homophyly is the mechanism of community
structures and a structural theory of networks. We proposed the notions of
entropy- and conductance-community structures. It was shown that the two
definitions of the entropy- and conductance-community structures and the notion
of modularity proposed by physicists are all equivalent in defining community
structures of networks, that neither randomness in the ER model nor
preferential attachment in the PA model is the mechanism of community
structures of networks, and that the existence of community structures is a
universal phenomenon in real networks. This poses a fundamental question: What
are the mechanisms of community structures of real networks? To answer this
question, we proposed a homophyly model of networks. It was shown that networks
of our model satisfy a series of new topological, probabilistic and
combinatorial principles, including a fundamental principle, a community
structure principle, a degree priority principle, a widths principle, an
inclusion and infection principle, a king node principle and a predicting
principle etc. The new principles provide a firm foundation for a structural
theory of networks. Our homophyly model demonstrates that homophyly is the
underlying mechanism of community structures of networks, that nodes of the
same community share common features, that power law and small world property
are never obstacles of the existence of community structures in networks, that
community structures are {\it definable} in networks, and that (natural)
communities are {\it interpretable}.

21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc