Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: \'Etude de l'omnipr\'esence des propri\'et\'es petit- monde et
  sans-\'echelle   The small-world and scale-free properties were identified in real-world
complex net-works at the end of the 90s. Their analysis led to a better
understanding of the dynamics and functioning of certain systems, and they were
studied in many subsequent works. This might be the reason why one frequently
finds, in the complex networks literature, assertions regarding their ubiquity,
their validity for almost all complex networks. Yet, the mentioned seminal
works were conducted on a very limited number of networks, and, to the best of
our knowledge, no large-scale study has been conducted to answer this question.
In this work, we take advantage, on the one hand, of the many datasets now
available online, to constitute a large collection of networks, and on the
other hand, of recent analysis tools, to check the validity of this hypothesis
of ubiquity. It turns out a large majority of the studied networks are indeed
small-world, how-ever this is not the case for the scale-free property, since
the degree distribution of a significant proportion of our networks does not
follow a power-law. MOTS-CL{\'E}S : R{\'e}seaux complexes, propri{\'e}t{\'e}s
topologiques, petit-monde, sans-{\'e}chelle.

8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom