Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantitative modeling of degree-degree correlation in complex networks   This paper presents an approach to the modeling of degree-degree correlation
in complex networks. Thus, a simple function, \Delta(k', k), describing
specific degree-to- degree correlations is considered. The function is well
suited to graphically depict assortative and disassortative variations within
networks. To quantify degree correlation variations, the joint probability
distribution between nodes with arbitrary degrees, P(k', k), is used.
Introduction of the end-degree probability function as a basic variable allows
using group theory to derive mathematical models for P(k', k). In this form, an
expression, representing a family of seven models, is constructed with the
needed normalization conditions. Applied to \Delta(k', k), this expression
predicts a nonuniform distribution of degree correlation in networks, organized
in two assortative and two disassortative zones. This structure is actually
observed in a set of four modeled, technological, social, and biological
networks. A regression study performed on 15 actual networks shows that the
model describes quantitatively degree-degree correlation variations.

6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex