Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sampling random graph homomorphisms and applications to network data
  analysis   A graph homomorphism is a map between two graphs that preserves adjacency
relations. We consider the problem of sampling a random graph homomorphism from
a graph $F$ into a large network $\mathcal{G}$. We propose two complementary
MCMC algorithms for sampling a random graph homomorphisms and establish bounds
on their mixing times and concentration of their time averages. Based on our
sampling algorithms, we propose a novel framework for network data analysis
that circumvents some of the drawbacks in methods based on independent and
neigborhood sampling. Various time averages of the MCMC trajectory give us
various computable observables, including well-known ones such as homomorphism
density and average clustering coefficient and their generalizations.
Furthermore, we show that these network observables are stable with respect to
a suitably renormalized cut distance between networks. We provide various
examples and simulations demonstrating our framework through synthetic
networks. We also apply our framework for network clustering and classification
problems using the Facebook100 dataset and Word Adjacency Networks of a set of
classic novels.

8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg