Research Of Weighted Complex Network Evolution Model And Vital Node

With the rapid development of network theory and computer technology, complex network is a new research direction in recent years. The study of complex network model mechanism and evolution can reveal common law in nature, biology, engineering and human society. How to reasonably reproduce the true evolution of complex network to accord with the real-world network characteristics is a core issue of complex network. In the complex network of application research, how to find important nodes and their importance (node importance), regardless of the improvement of invulnerability and reliability of complex network, or the destruction of the enemy target network, have important theoretical significance and application value.This thesis focuses on modeling complex network and estimating important nodes and the contributions of this thesis are as follows:1. Basing on the BBV scale-free model and the local-world model, we building a new BBV based on local-world evolving model which not only takes into account of adding new nodes, but also takes into account of adding and removing edges in the local-world, the adding edges between the local-worlds. According to continuum theory, we obtain the strength distribution of nodes and the exponent of power-law can be adjusted between 2 to 3 with regulating the parameters, which accord with power-law exponent in the realistic networks. The analytical expression is in good agreement with the numerical calculations.2. We analyze two indicators of influencing the importance of the nodes: node weight and node location.According to two indicators, we propose a weight reducted method of identifying important nodes in the weighting network and unweighting network. We propose an improved method of node removed method which is in good agreement with weight reducted method.We analyze the time complexity of two methods. If we choose the appropriate shortest path algorithm, we can get a better time complexity. We study weighting network and propose a definition of survivability of network basing on weight reducted method which can distinguish and quantize different survivability of networks.