Research On Scale-free Network Modeling And Invulnerability

The Complex network is an important tool of investigating the structure andfunction of all kinds of complex systems in nature and society. How to reveal theregulation of realistic network system via the research of the complicated networkmodels has become an emerging hotspot. In recent years, scale-free property has beendiscovered from many real-world networks such as Internet networks, www networks,wealth distribution networks and so on. So it is very necessary to study the scale-freenetwork model in depth. In addition, due to the scale-free property of complex networkmakes it very fragile to the deliberate attacks. Therefore, locating the key nodes andprotecting them through node importance assessment plays an important role in themaintenance of the entire network survivability. Then, the paper discusses a networkinvulnerability assessment approach based on the network entropy of node importance.This paper focuses on the following three sections. Section Ⅰ improves thescale-free network and proposes a simple hybrid evolutionary network model based onthe node fitness and mixed even side, the continuous domain method is used to calculatethe distribution of improved model. Through theoretical analysis and simulation, it isfound that the degree distribution is no longer a power-law distribution in the doublelogarithmic coordinate plane, and it is more in line with the evolution of the realisticnetwork than the usual BA model in terms of the average shortest path length and theclustering coefficient. Section Ⅱ defines a node importance function based on the nodeconnectivity degree and local connectivity. The index of the node importance function issubstantially consistent with the index of the average shortest path in networks, theimportance of each node in the network can be sorted by the size of the index value. Forsmall networks, it is relatively simple in calculation, the method is verified moreintuitive, effective and reasonable by theoretical analysis and practical examples.Section Ⅲ discusses a network invulnerability assessment approach based on thenetwork entropy of node importance, and compared with the current networkinvulnerability assessment approach based on the network entropy of node connectivity,the results show that the former has certain advantages.