Invulnerability Optimization And Evaluation Techniques Of Complex Network

Network with some or all of the natures of self-organization, self-similarity, small world, scale-free is the complex network. The complexity of the nature and social can be attributed to the complexity of the network interwoven, through which, the various components of the system turn to be various dominant, nonlinear effect between them. In recent years, the reaearch on complex networks came into being, which is just the rise of a new direction. In the course of the study of complex networks, scientists have found that the degree of complex network follows the power law distribution, that is, the node degree K with respect to its probability P(K) meet the power law relationship, and the power exponent ranges from 2 to 3. Network with such properties has a special name:scale-free network. Here the scale-free means the network lakes a feature value (or an average value of degree), that is, the node degree range value flucted considerablely.The pawer law properties of complex network makes it is fragile to the deliberate attacks, that is when attack only a few key nodes can cause the network parlay, while it is very robust to the random attacks. The complex network has the properties of'Robust-yet-Fragile', therefore, more and more research institution focus their attention on the network invulnerability.At present, many issues of the research on network invulnerability need to be investigated immediately, such as follows:1) there is no deeply understanding of the nature characteristics of the network topology:it needs to have a deeply understanding to study the problem of the complex network invulnerability. Learn the main cause of the pawer law and solve the problem in the complex network by the way of learning the development of the internal law of network.2) The present optimization of network invulnerability limited in the Picture Theory and the Mathematical, which can not seize the internal development laws of the network, which ignores the impact of the network invulnerability as the cause of the network.3) The present cascading models do not consider the attributes of the nodes.4) The existing network invulnerability evaluation criteria are too complex, lacking a simple and effective assessment of invulnerability technology.This thesis focuses on the issuses above and carries out the follows research:1) Researched the HOT(Highly Optimized Tolerance/Tradeoff) theory and the cause of the pawer law from the perspective of system optimization. Pawer law is a common phenomenon in complex networks, and there are many theories to explain its cause. This thesis explained how to get a power law distribution output by HOT optimization process through a simple model of fire forest, and summarized the applications of HOT thery on system optimization and modeling of the network.2) Porposed the invulnerable dynamic evoluation model of network based on HOT theory. A key aspect of complex systems that has been a main theme of HOT is the relationship between robustness and fragility. System should be robust to uncertainties in their environment, while the ensuing complexity makes these systems robust to the uncertainties for which such complexity was selected. This thesis solved the problem of building the invulnerable dynamic evolution model of the network as a HOT problem, and through the nodes preference attachment scheme, the invulnerability and self-recovery capabilities etc. of the system could evolve toward the optimal direction. Theoretical analysis shows that the node can adjust its properties to generate the invulnerable dynamic evolution model with power law distribution of node degree; simulation analysis indicates that the HOT model has a better invulnerability than that of BA model.3) Proposed a model for cascading network failures based on the nodes with different tolerance parameter. We proposed a simple model for cascading failures in the network to explore how the failures can have a great impact on the network performance, and allocated every node a Ci by the tolerance parameterαbased on the node importance IMP, and the IMP is determined by the node degree K, the number of the shortest paths S through a node, and the number of the shortest paths Ne through the neighbors of a node, then we fix every element a weight to compute the IMP by the AHP (Analytic Hierarchy Process) theory. Based on the model, we analyzed the influence of different types of attacks to the network performance, and also tabled some proposals for reducing the damage the networks suffered from the cascading failures.4) Proposed a network invulnerability assessment techniques based on the network entropy of node importance. The network scale-free characteristic is actually a non-homogeneous, which is, most of the nodes have a small number of connections while few of the nodes have a large number of connections. The uneven distribution of the node degree lead the network can not effectively resistant the deliberately attacks, which can reflect the ability of the network invulnerability in a certain extent. This thesis proposed a network invulnerability assessment techniques based on the network entropy of node importance, in which the node importance is consist of the constant and variable part, which can measure the node importance when the network changes. By comparing the network entropy after the attack with its initial entropy, this method can assess the network invulnerability effectively.