Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effect of degree correlations above the first shell on the percolation
  transition   The use of degree-degree correlations to model realistic networks which are
characterized by their Pearson's coefficient, has become widespread. However
the effect on how different correlation algorithms produce different results on
processes on top of them, has not yet been discussed. In this letter, using
different correlation algorithms to generate assortative networks, we show that
for very assortative networks the behavior of the main observables in
percolation processes depends on the algorithm used to build the network. The
different alghoritms used here introduce different inner structures that are
missed in Pearson's coefficient. We explain the different behaviors through a
generalization of Pearson's coefficient that allows to study the correlations
at chemical distances l from a root node. We apply our findings to real
networks.

23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con