Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase transitions in edge-weighted exponential random graphs   The exponential family of random graphs represents an important and
challenging class of network models. Despite their flexibility, conventionally
used exponential random graphs have one shortcoming. They cannot directly model
weighted networks as the underlying probability space consists of simple graphs
only. Since many substantively important networks are weighted, this limitation
is especially problematic. We extend the existing exponential framework by
proposing a generic common distribution for the edge weights and rigorously
analyze the associated phase transitions and critical phenomena. We then apply
these general results to get concrete answers in exponential random graph
models where the edge weights are uniformly distributed.

37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg