Research On Node Centrality Measurement Based On Page Rank In Multi-dimensional Networks

The related research on complex networks is of great significance to all aspects of social life.With the continuous deepening of its related research and the rapid development of social information,the original one-dimensional network with only one connection between the nodes cannot meet the real-world application requirements.As a result,the research on complex networks has gradually shifted to multi-dimensional networks where nodes have multiple connection relationships.There have been many research results on node centrality measurement methods in one-dimensional networks.However,these methods are not effective in multi-dimensional networks,and lack the measurement of the influence of various dimensions on node centrality.Therefore,the centrality measurement method in the one-dimensional network may not be applicable in the multi-dimensional network.At present,in the related research of node centrality measurement methods in multi-dimensional networks,a class of measurement methods based on PageRank algorithm comprehensively considers the influence of dimensions on node centrality,which has important reference value.Aiming at the problem of measuring the centrality of nodes in a multi-dimensional network,based on related research,this paper proposes a Multi-PageRank algorithm based on the PageRank idea.First,an algorithm for calculating the local migration tendency between dimensions is proposed,and the result of this operation provides the basis for the centrality allocation of nodes in the subsequent Multi-PageRank algorithm.At the beginning of the calculation of the local migration tendency between dimensions,considering that the walking process is only affected by the local area where the random walker is currently located,a local multi-dimensional network and the local walking probability are defined.Based on this,the relative entropy is used to measure the local difference between the dimensions.And then get the local migration tendency between dimensions.Secondly,based on the local migration tendency between dimensions,the inter-dimensionmigration probability matrix is constructed,then the dissimilarity between the multi-dimensional network and the corresponding extreme network is calculated,after the multi-dimensional network difficulty probability is obtained,and the simple center of the nodes in the multi-dimensional network is obtained by this coefficient.Thirdly,the initial extreme network construction method is given,and the variation trend of dissimilarity is analyzed.By quickly selecting a small number of extreme networks with small dissimilarities to approximate the probability of difficulty,the problem of too large a time cost for the probability calculation of the difficulty when the network dimension is high is solved.Finally,a Multi-PageRank algorithm is presented to measure the centrality of nodes in a multi-dimensional network.This paper conducts comparative experiments on five multi-dimensional networks.The experimental results show that the algorithm has several advantages:the centrality ranking of the nodes obtained on each network is more reasonable;by adjusting the local network radius,the local network can be more accurately reflected the impact of structure on node centrality;by approximating the probability of dilemma,you can process high-dimensional network data more quickly with minimal impact on the calculation of node centrality,and ensure computing efficiency while obtaining a reasonable ranking.