Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-similarity of complex networks   Complex networks have been studied extensively due to their relevance to many
real systems as diverse as the World-Wide-Web (WWW), the Internet, energy
landscapes, biological and social networks
\cite{ab-review,mendes,vespignani,newman,amaral}. A large number of real
networks are called ``scale-free'' because they show a power-law distribution
of the number of links per node \cite{ab-review,barabasi1999,faloutsos}.
However, it is widely believed that complex networks are not {\it length-scale}
invariant or self-similar. This conclusion originates from the ``small-world''
property of these networks, which implies that the number of nodes increases
exponentially with the ``diameter'' of the network
\cite{erdos,bollobas,milgram,watts}, rather than the power-law relation
expected for a self-similar structure. Nevertheless, here we present a novel
approach to the analysis of such networks, revealing that their structure is
indeed self-similar. This result is achieved by the application of a
renormalization procedure which coarse-grains the system into boxes containing
nodes within a given "size". Concurrently, we identify a power-law relation
between the number of boxes needed to cover the network and the size of the box
defining a finite self-similar exponent. These fundamental properties, which
are shown for the WWW, social, cellular and protein-protein interaction
networks, help to understand the emergence of the scale-free property in
complex networks. They suggest a common self-organization dynamics of diverse
networks at different scales into a critical state and in turn bring together
previously unrelated fields: the statistical physics of complex networks with
renormalization group, fractals and critical phenomena.

19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
2
The categories of this paper are: math