Complex Network Topology Anti-destroying Ability Research

Human life is inseparable from the network, people need different networkeveryday. When people travel, they need rail transportation network. Rail transportationnetwork is composed of bus station and bus lines. When people want to get information,they need the Internet. The Internet is composed of many routers between them and thecable connection components. When people send messages by email, they need acontact network. The contacts and links between them established a mail receiving andsending network. The complexity of the network has puzzled scientists. When thenumber of network nodes is larger, the more complex the network, however, peoplecannot evasive network.How to judge a network have a good invulnerability? When a network in the faceof natural disasters or sabotage, how is its reliability? How to transform the existingnetwork to make it safer? In the case of network is destroyed, how to realize thenetwork recovery? This paper is to address the problem. Complex network is the mainresearch object. The complex network invulnerability is studied. Main contents:(1) We present a complex network invulnerability measure index called Pd.We propose a new complex network invulnerability measure index Pd. It isdefined as: when a node under the network attack, network on the brink of collapse, thenetwork attack edge accounted for the proportion of the number of edges, denoted Pd.In the face of certain network attack mode, the percentage of P edges are removed,when P exceeds a certain threshold, the P> Pd, the network breakdown into many smallnon-connected region, when P <Pd, network contain a complete connected region. Pdmakes scientists have another metric. In realistic networks, edges sometimes moreimportant than point. The percentage of edge removal could be better, morecomprehensive assessment of network invulnerability.(2) We studied the entropy of degree distribution in a malicious attack to optimizecomplex network invulnerability.Complex network in the face of malicious attacks, often show weakinvulnerability, in the face of random failure, survivability is strong, so malicious attack model for the study of complex network invulnerability is very important. I study theentropy of degree distribution in a malicious attack on complex network invulnerabilityoptimization. Through computer simulation and theoretical deduction, I found that theentropy of degree distribution can optimize complex network. Prove that the degreedistribution entropy in malicious attacks case of network optimization is equivalent tothe maximization of the entropy of degree distribution. At the same time, we extendresearch results to a random failure cases, prove that the degree distribution entropy inrandom failure cases and malicious attack cases, optimization equivalent to the Pdinvulnerability metric network invulnerability. Therefore, entropy of degree distributioncan be used as a measure of network survivability. Since the entropy of degreedistribution react network heterogeneity degree, we find a heterogeneous network canmeasure network invulnerability.(3) We propose a method to improve the network invulnerability by increasinglink redundancy between key nodes.We found by simulation and theoretical derivation that our method better than theprevious method. When the network breakdown, we labeled the degree of max-degreeremaining nodes in the original network is K. We define key node as follow: the nodeswhose degree is K-2. We find network survivability has been greatly upgrade byincreasing the redundancy links between key nodes.(4) We proposed a protecting key node method to increase the networksurvivability.Because the key nodes are very important to network survivability, so we proposea key nodes protection strategy. Through the protection of key nodes, we make thenetwork survivability significantly improved. The protection of key nodes in the realnetwork is very easy to achieve. These nodes are very important to us, but at the sametime, they are normal nodes for attacker. The key nodes can be hidden to attacker.