Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Error and attack tolerance of complex networks   Many complex systems, such as communication networks, display a surprising
degree of robustness: while key components regularly malfunction, local
failures rarely lead to the loss of the global information-carrying ability of
the network. The stability of these complex systems is often attributed to the
redundant wiring of the functional web defined by the systems' components. In
this paper we demonstrate that error tolerance is not shared by all redundant
systems, but it is displayed only by a class of inhomogeneously wired networks,
called scale-free networks. We find that scale-free networks, describing a
number of systems, such as the World Wide Web, Internet, social networks or a
cell, display an unexpected degree of robustness, the ability of their nodes to
communicate being unaffected by even unrealistically high failure rates.
However, error tolerance comes at a high price: these networks are extremely
vulnerable to attacks, i.e. to the selection and removal of a few nodes that
play the most important role in assuring the network's connectivity.

12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
16
The categories of this paper are: stat