Complex Network Reliability Analysis based on Entropy Theory

Network reliability is an essential issue of complex networks; the reliability of complex networks plays an important role in the performance in the research process. At the same time, the number of connected nodes in a complex network is a main measure of the complex network. Due to the randomness of complex networks, we define one new degree sequence and the entropy of the complex network, and we then study the entropy of the network as a new measure for the network reliability. The features of entropy are studied in complex networks, and entropy is analyzed in two representative complex network models, the random network model and scale-free network model. The degree distributions functions in the random network model and scale-free network model have significantly different characteristics, the Poisson distribution and Power-law distribution. Furthermore, we study the entropy features under two nodes fault models, random failures and deliberate attacks. We discuss the entropy of the random network model and scale-free network model in two fault modes with the fault intensity gradually increasing from 0 to 1.0. Then, we study the relation between the average degree distribution and the entropy of the network when the fault intensity is 0.3. The results show that the entropy of the network is reasonable to measure the network reliability similar to the number of connected nodes in the network. The purpose of the research is to provide a new way to study network reliability.