Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local cluster aggregation models of explosive percolation   We introduce perhaps the simplest models of graph evolution with choice that
demonstrate discontinuous percolation transitions and can be analyzed via
mathematical evolution equations. These models are local, in the sense that at
each step of the process one edge is selected from a small set of potential
edges sharing common vertices and added to the graph. We show that the
evolution can be accurately described by a system of differential equations and
that such models exhibit the discontinuous emergence of the giant component.
Yet, they also obey scaling behaviors characteristic of continuous transitions,
with scaling exponents that differ from the classic Erdos-Renyi model.

1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph