摘要
With a simple model, we study the stability of random networks under the evolution of attack and repair. We introduce a new quantity, i.e. invulnerability I（s）, to describe the stability of the system. It is found that the network can evolve to a stationary state. The stationary value Ic has a power-law dependence on the initial average degree （κ）, with the slope about -1.5. In the stationary state, the degree distribution is a normal distribution, rather than a typical Poisson distribution for general random graphs. The clustering coefficient in the stationary state is much larger than that in the initial state. The stability of the network depends only on the initial average degree （κ）, which increases rapidly with the decrease of （κ）.
With a simple model, we study the stability of random networks under the evolution of attack and repair. We introduce a new quantity, i.e. invulnerability I（s）, to describe the stability of the system. It is found that the network can evolve to a stationary state. The stationary value Ic has a power-law dependence on the initial average degree （κ）, with the slope about -1.5. In the stationary state, the degree distribution is a normal distribution, rather than a typical Poisson distribution for general random graphs. The clustering coefficient in the stationary state is much larger than that in the initial state. The stability of the network depends only on the initial average degree （κ）, which increases rapidly with the decrease of （κ）.
基金
Supported in part by the National Natural Science Foundation of China under Grant Nos 70271067 and 70401020, and the Ministry of Education of China under Grant No 03113.
