Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal map of the modular structure of complex networks   Modular structure is pervasive in many complex networks of interactions
observed in natural, social and technological sciences. Its study sheds light
on the relation between the structure and function of complex systems.
Generally speaking, modules are islands of highly connected nodes separated by
a relatively small number of links. Every module can have contributions of
links from any node in the network. The challenge is to disentangle these
contributions to understand how the modular structure is built. The main
problem is that the analysis of a certain partition into modules involves, in
principle, as many data as number of modules times number of nodes. To confront
this challenge, here we first define the contribution matrix, the mathematical
object containing all the information about the partition of interest, and
after, we use a Truncated Singular Value Decomposition to extract the best
representation of this matrix in a plane. The analysis of this projection allow
us to scrutinize the skeleton of the modular structure, revealing the structure
of individual modules and their interrelations.

4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat