Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase Transition of the 2-Choices Dynamics on Core-Periphery Networks   Consider the following process on a network: Each agent initially holds
either opinion blue or red; then, in each round, each agent looks at two random
neighbors and, if the two have the same opinion, the agent adopts it. This
process is known as the 2-Choices dynamics and is arguably the most basic
non-trivial opinion dynamics modeling voting behavior on social networks.
Despite its apparent simplicity, 2-Choices has been analytically characterized
only on restricted network classes---under assumptions on the initial
configuration that establish it as a fast majority consensus protocol.
  In this work, we aim at contributing to the understanding of the 2-Choices
dynamics by considering its behavior on a class of networks with core-periphery
structure, a well-known topological assumption in social networks. In a
nutshell, assume that a densely-connected subset of agents, the core, holds a
different opinion from the rest of the network, the periphery. Then, depending
on the strength of the cut between the core and the periphery, a
phase-transition phenomenon occurs: Either the core's opinion rapidly spreads
among the rest of the network, or a metastability phase takes place, in which
both opinions coexist in the network for superpolynomial time. The interest of
our result is twofold. On the one hand, by looking at the 2-Choices dynamics as
a simplistic model of competition among opinions in social networks, our
theorem sheds light on the influence of the core on the rest of the network, as
a function of the core's connectivity toward the latter. On the other hand, we
provide one of the first analytical results which shows a heterogeneous
behavior of a simple dynamics as a function of structural parameters of the
network. Finally, we validate our theoretical predictions with extensive
experiments on real networks.

2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ