An Effective Method to Improve the Resistance to Frangibility in Scale-Free Networks

The scale-free networks reveals the essential characteristics of networks, which can be used to describe many realistic networks, which has a common features: The minority vertices have massive connections, the number of which may reach as high as several million, but the majority vertices only have few connections, which is one of characteristics of scale-free networks. So the scale-free networks were robust when nodes were moved randomly but frangible when nodes were attacked spitefully. If the networks ´ degree distribution is uniform, which may enhance the vulnerability capacity of the scale-free networks. Therefore this paper embarks from hubs and the minimum degree the two aspects to improve scale-free networks´ anti-frangibility ability. To improve the resistance to frangibility in scale free networks, a model based on endurable probability and entropy of degree distribution was proposed in this paper. In order to control the hubs, a method was put forward to measure off rank. We focused on the key nodes, which a certain nodes should be protected and a certain connections should be partitioned and reconstructed. Compare with the original structure, the optimized structure was smarter, more tolerant of wrong and resistant of frangibility. The simulation showed that the minimum degree of scale free networks was set and coordinated properly, which could mend the resistance to frangibility. And the topology of scale-free networks was optimized and the work efficiency and resist of frangibility were also improved.