H-index Of Directed Weighted Network And Network Model Construction

Directed weighted networks are a more complex and practical type of complex networks.Based on this,this paper studies the importance of nodes in directed weighted networks,focusing on h-index family indicators.The article is developed from the following aspects:Firstly,due to the direction and weight of the edges,we extend the h-index to the directed weighted network,and redefine the general degree,h-index and coreness of the nodes,and propose a general methodological framework,which not only integrates the “in” information and “out” information of the network,but also contains the different definition methods of degree.In addition,theoretical analysis shows that there is an internal connection between the three.The relationship indicates that the general degree of the node can be regarded as the initial state,each order h-index of the node can be regarded as the intermediate state,the coreness of the node can be regarded as the steady state of the node.Meanwhile,we designed the algorithm of the aforementioned method,and gave several examples and the application of the real networks.The results show that the first-order h-index(that is,the commonly referred to H-index)can better characterize the importance of the "hub" node in the network.Secondly,a directed weighted scale-free network is constructed based on the strength of the node instead of the degree of the node,and the network generation algorithm is given.The algorithm introduces a weight adaptive evolution mechanism while maintaining the growth characteristics and preferential attachment mechanism.Furthermore,both theoretical and numerical analysis demonstrate that the directed weighted scale-free network generated by the algorithm does accord with the power law characteristics,and the power law exponent without reference to the network size,but related to the initial parameters of the model.Thirdly,on the basis of an ideal directed weighted scale-free network model,in order to explore the statistical characteristics of a certain type of real network,we constructed the scale-free network model based on real network information.Furthermore,we apply the general method framework of h-index to the network model to calculate the importance of nodes in the network.