Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Correlated random networks   We develop a statistical theory of networks. A network is a set of vertices
and links given by its adjacency matrix $\c$, and the relevant statistical
ensembles are defined in terms of a partition function $Z=\sum_{\c} \exp
{[}-\beta \H(\c) {]}$. The simplest cases are uncorrelated random networks such
as the well-known Erd\"os-R\'eny graphs. Here we study more general
interactions $\H(\c)$ which lead to {\em correlations}, for example, between
the connectivities of adjacent vertices. In particular, such correlations occur
in {\em optimized} networks described by partition functions in the limit
$\beta \to \infty$. They are argued to be a crucial signature of evolutionary
design in biological networks.

33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn