Node Importance Evaluation And Its Application Research In Complex Networks

There are many phenomenons associated with the node importance in complex networks. To identify important nodes and evaluate their importance have high practical value.Therefore, how to quantify the importance of the node is a basic problem.This thesis first elaborates three research method of this problem, then thorough analysis and compares several famous evaluation indexes, propose an evaluation index for node importance based on mutual information. This index reference the mutual information viewpoint in information theory, simultaneously considers the topology characteristic and the importance feedback from neighbors. The experiment results show that the evaluation method based on mutual information is simple and effective.Then this thesis carries on the actual application of the node importance.Complex network model optimization:BA scale-free network model ignores the appraisal which the node obtains in the network evolution. In the real system, new nodes tend to connect the nodes have been highly recognized, usually these nodes are the important nodes. Therefore the paper presents a scale-free network model based on pagerank algorithm. The simulation experiments confirm the degree distribution of the model consistency with the theoretical derivation, and show that the new model has smaller cluster coefficient and bigger average path length than BA model.Clustering algorithms of complex networks:Important nodes have a bigger influence area, so we can use the attraction of important nodes to clustering. This thesis reference the data field ideology from Cognitive Physics, present a clustering algorithm based on the mutual information index, simulation experiments show that this algorithm in calculation accuracy and time all have good performance.