Analysis Of Robustness And Fragility For Probability Routing Strategy On Scale-free Network

Nowadays the networks have played more and more important role in our daily lives.Several of networks have proved to be scale-free,such as Internet,WWW,large power network,global transportation network,metabolism network,research cooperation network and social networks.It is an inevitable problem for network congestion,which will cause inconvenience to people's lives and huge losses to the national economy.It is of great practical significance to improve network capacity by studying congestion problems on the scale-free networks.While the feasible way to improve the communication performance of networks is to optimize the routing strategies,which arouse wide attention of scholars.At present,many effective routing strategies have been proposed on fixed networks,greatly improving the network capacity.In fact,networks will always be subject to deliberate attacks or unintentional power failure and other damages to the network topology.Whether the previous routing strategies still has a high network capacity when the networks are destroyed,which is worth in further study.In this paper,we adopt the network capacity and the average path length as criteria to measure the routing strategies.Associate professor Xiaojun Zhang had confirmed that the probability routing strategy has highest network capacity and shorter average path length among the shortest-path routing strategy and efficient routing strategy on scale-free networks.We mainly focus on the robustness and fragility of the probability routing strategy in random attack and deliberate attack on scale-free networks.Once the scale-free networks are attacked,the robustness and fragility of the probability routing strategy are considered in two cases according to the recovery of routing path.1 In the first case,the networks are difficult to recover when attacked,so the routing path of packets should be re-defined.Therefore,the network capacity and average path length in the giant component are considered.2 In the second case,we assume that the routing path too late to adjust in the initial stage of the network attack.As a result,the network capacity and average path length should be considered on the whole network.In this paper,we adopt a method of random failures and selecting failures deleting nodes to simulate random attacks and intentional attacks on a scale-free network.Byrandomly removing 0-10% of the nodes simulates the scale-free networks suffered random attacks.Firstly,the nodes in the scale-free network are sorted according to degree descending order,then deleting 0-10% large nodes to simulate deliberate attacks.Finally,the MATLAB simulation experiments show the curve between network capacity and average path length with the proportion of deletion nodes.We could obtain the stability and fragility of probability routing strategy when the scale-free network encounter random attacks and target attacks.In order to make the conclusion general,we analyze the change of the network size and the network average degree how they affect the stability and vulnerability of probability routing strategy.