Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of maximum likelihood estimates in exponential random graph
  models   We present a streamlined proof of the foundational result in the theory of
exponential random graph models (ERGMs) that the maximum likelihood estimate
exists if and only if the target statistic lies in the relative interior of the
convex hull of the set of realizable statistics. We also discuss how linear
dependence or "approximate linear dependence" of network statistics may lead to
degeneracy during model fitting.

24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess