Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological Graph Persistence   Graphs are a basic tool for the representation of modern data. The richness
of the topological information contained in a graph goes far beyond its mere
interpretation as a one-dimensional simplicial complex. We show how topological
constructions can be used to gain information otherwise concealed by the
low-dimensional nature of graphs. We do that by extending previous work of
other researchers in homological persistence, by proposing novel
graph-theoretical constructions. Beyond cliques, we use independent sets,
neighborhoods, enclaveless sets and a Ramsey-inspired extended persistence.

20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics