Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Degree correlations in directed scale-free networks   Scale-free networks, in which the distribution of the degrees obeys a
power-law, are ubiquitous in the study of complex systems. One basic network
property that relates to the structure of the links found is the degree
assortativity, which is a measure of the correlation between the degrees of the
nodes at the end of the links. Degree correlations are known to affect both the
structure of a network and the dynamics of the processes supported thereon,
including the resilience to damage, the spread of information and epidemics,
and the efficiency of defence mechanisms. Nonetheless, while many studies focus
on undirected scale-free networks, the interactions in real-world systems often
have a directionality. Here, we investigate the dependence of the degree
correlations on the power-law exponents in directed scale-free networks. To
perform our study, we consider the problem of building directed networks with a
prescribed degree distribution, providing a method for proper generation of
power-law-distributed directed degree sequences. Applying this new method, we
perform extensive numerical simulations, generating ensembles of directed
scale-free networks with exponents between~2 and~3, and measuring ensemble
averages of the Pearson correlation coefficients. Our results show that
scale-free networks are on average uncorrelated across directed links for three
of the four possible degree-degree correlations, namely in-degree to in-degree,
in-degree to out-degree, and out-degree to out-degree. However, they exhibit
anticorrelation between the number of outgoing connections and the number of
incoming ones. The findings are consistent with an entropic origin for the
observed disassortativity in biological and technological networks.

7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom