Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Core percolation on complex networks   As a fundamental structural transition in complex networks, core percolation
is related to a wide range of important problems. Yet, previous theoretical
studies of core percolation have been focusing on the classical
Erd\H{o}s-R\'enyi random networks with Poisson degree distribution, which are
quite unlike many real-world networks with scale-free or fat-tailed degree
distributions. Here we show that core percolation can be analytically studied
for complex networks with arbitrary degree distributions. We derive the
condition for core percolation and find that purely scale-free networks have no
core for any degree exponents. We show that for undirected networks if core
percolation occurs then it is always continuous while for directed networks it
becomes discontinuous when the in- and out-degree distributions are different.
We also apply our theory to real-world directed networks and find,
surprisingly, that they often have much larger core sizes as compared to random
models. These findings would help us better understand the interesting
interplay between the structural and dynamical properties of complex networks.

7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ