Research Of The Average Betweenness Of Network

Betweenness in complex networks is one of the importance index to expressionnode or edge. The influence of network nodes or edges can be divided into nodesbetweenness and edges betweenness. Betweenness of node is the proposition of theshortest path between any two nodes through the node numbers and the all shortestpath numbers in the network, betweenness of edge is the proposition of the shortestpath between any two nodes through the edge numbers and the all shortest pathnumbers in the network, too. The average node betweenness of network is refers tothe average numbers of all nodes betweenness in the network and the same to theedge betweenness. The node betweenness in tree network is through the node pathnumbers. In this paper, we mainly discuss the average betweenness in tree network.This paper characterize the trees with the maximum and minimum averagebetweenness. And calculate the value of M Tree node betweenness in differentsituations. The simulation results of the statistical betweenness of Tree network indifferent nodes.The specific arrangement of the thesis are as follows.In chapter1, we introduce the present situation of research and development ofcomplex network. Some main results are listed.In chapter2, some of the concepts, definitions and lemmas involved in this thesisare listed, partial theories and formulas used in the calculation of the main results ofthis paper are presented.In chapter3, we main introduce the Tree network with the maximum andminimum average node betweenness. At the same time for the maximum and theminimum edge betweenness of network are given.In chapter4, For the betweenness has N nodes of the M tree is calculated, and forthe different branches of the situation, this paper presents a method to calculate theresults.We summarize and discuss some problems in the future in last chapter.