Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic statistics for a directed random graph model with
  reciprocation   The p_1 model is a directed random graph model used to describe dyadic
interactions in a social network in terms of effects due to differential
attraction (popularity) and expansiveness, as well as an additional effect due
to reciprocation. In this article we carry out an algebraic statistics analysis
of this model. We show that the p_1 model is a toric model specified by a
multi-homogeneous ideal. We conduct an extensive study of the Markov bases for
p_1 models that incorporate explicitly the constraint arising from
multi-homogeneity. Our results are directly relevant to the estimation and
conditional goodness-of-fit testing problems in p_1 models.

28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat