Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Emergence of Long-Range Correlations in Random Networks   We perform an analytical analysis of the long-range degree correlation of the
giant component in an uncorrelated random network by employing generating
functions. By introducing a characteristic length, we find that a pair of nodes
in the giant component is negatively degree-correlated within the
characteristic length and uncorrelated otherwise. At the critical point, where
the giant component becomes fractal, the characteristic length diverges and the
negative long-range degree correlation emerges. We further propose a
correlation function for degrees of the $l$-distant node pairs, which behaves
as an exponentially decreasing function of distance in the off-critical region.
The correlation function obeys a power-law with an exponential cutoff near the
critical point. The Erd\H{o}s-R\'{e}nyi random graph is employed to confirm
this critical behavior.

7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph