Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase transitions in social networks inspired by the Schelling model   We propose two models of social segregation inspired by the Schelling model.
Agents in our models are nodes of evolving social networks. The total number of
social connections of each node remains constant in time, though may vary from
one node to the other. The first model describes a "polychromatic" society, in
which colors designate different social categories of agents. The parameter
$\mu$ favors/disfavors connected "monochromatic triads", i.e. connected groups
of three individuals \emph{within the same social category}, while the
parameter $\nu$ controls the preference of interactions between two individuals
\emph{from different social categories}. The polychromatic model has several
distinct regimes in $(\mu,\nu)$-parameter space. In $\nu$-dominated region, the
phase diagram is characterized by the plateau in the number of the inter-color
connections, where the network is bipartite, while in $\mu$-dominated region,
the network looks as two weakly connected unicolor clusters. At
$\mu>\mu_{crit}$ and $\nu >\nu_{crit}$ two phases are separated by a critical
line, while at small values of $\mu$ and $\nu$, a gradual crossover between the
two phases occurs. The second "colorless" model describes a society in which
the advantage/disadvantage of forming small fully connected communities (short
cycles or cliques in a graph) is controlled by a parameter $\gamma$. We analyze
the topological structure of a social network in this model and demonstrate
that above a critical threshold, $\gamma^+>0$, the entire network splits into a
set of weakly connected clusters, while below another threshold, $\gamma^-<0$,
the network acquires a bipartite graph structure. Our results propose
mechanisms of formation of self-organized communities in international
communication between countries, as well as in crime clans and prehistoric
societies.

26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
2
The categories of this paper are: math
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex