Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A methodology to evaluate the evolution of networks using topological
  data analysis   Networks are important representations in computer science to communicate
structural aspects of a given system of interacting components. The evolution
of a network has several topological properties that can provide us information
on the network itself. In this paper, we present a methodology to compare the
the topological characteristics of the evolution of a network, encoded into a
(persistence) diagram that tracks the lifetimes of those features. This will
enable us to classify the evolution of networks based on the distance between
the diagrams that represent such network evolution. In that, we also consider
complex vectors that bring a complementary perspective to the distance-based
classification that is closer to the computational methods, aims to enhance the
computational efficiency of those comparisons, and that is by itself a source
of open research questions.

34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio