Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effect of degree correlations on the loop structure of scale-free
  networks   In this paper we study the impact of degree correlations in the subgraphs
statistics of scale-free networks. In particular we consider loops: a simple
case of network subgraphs which encode the redundancy of the paths passing
through every two nodes of the network. We provide an understanding of the
scaling of the clustering coefficient in modular networks in terms of the
eigenvector of the correlation matrix associated with the maximal eigenvalue
and we show that correlations affect in a relevant way the average number of
Hamiltonian paths in a 3-core of real world networks. We prove our results in
the two point correlated hidden variable ensemble and we check the results with
exact counting of small loops in real graphs.

10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs