Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of complex networks under the evolution of attack and repair   With a simple attack and repair evolution model, we investigate and compare
the stability of the Erdos-Renyi random graphs (RG) and Barabasi-Albert
scale-free (SF) networks. We introduce a new quantity, invulnerability I(s), to
describe the stability of the system. We find that both RG and SF networks can
evolve to a stationary state. The stationary value Ic has a power-law
dependence on the average degree <k>_rg for RG networks; and an exponential
relationship with the repair probability p_sf for SF networks. We also discuss
the topological changes of RG and SF networks between the initial and
stationary states. We observe that the networks in the stationary state have
smaller average degree <k> but larger clustering coefficient C and stronger
assortativity r.

14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci