Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Resilience of the Internet to random breakdowns   A common property of many large networks, including the Internet, is that the
connectivity of the various nodes follows a scale-free power-law distribution,
P(k)=ck^-a. We study the stability of such networks with respect to crashes,
such as random removal of sites. Our approach, based on percolation theory,
leads to a general condition for the critical fraction of nodes, p_c, that need
to be removed before the network disintegrates. We show that for a<=3 the
transition never takes place, unless the network is finite. In the special case
of the Internet (a=2.5), we find that it is impressively robust, where p_c is
approximately 0.99.

12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas