Research On Important Node Identification Method Of Hypernetwork Based On Network Entropy

With the continuous development of 5G network and online platform,the characteristics of“groupization”of network individuals are emerging:In social network level,the discussion of network community has become a universal phenomenon;in the level of scientific cooperation,it is embodied in the organization of a paper.With its“multivariate”structure,hypergraph breaks the limitation of“binary interaction”in traditional network structure,so as to specifically depict the multiple features of the real system and the interaction and influence relations among the multiple elements.As one of the effective ways to explore and reveal the intrinsic mechanisms of complex systems,the identification of significant nodes in hypernetwork has been widely studied and applied.However,among the currently known important node identification methods,most of them are based on a single index of network topology,which can only reflect part of the information of nodes from a certain aspect,ignoring the influence of neighbor nodes and even the whole network nodes on the evaluation nodes,while the overall statistical characteristics of the network are not considered.In view of this,based on the network entropy,this paper studies the identification of important nodes in hypernetwork as follows:(1)A multi-attribute decision-making method based on entropy to identify important nodes in hypernetworks.The local influence and global influence of nodes play an important role in the recognition of node importance.Based on the K-shell method of hypernetwork,this paper considers the node’s own attributes and introduces the influence of neighbor nodes on its own node,and proposes two indicators:local influence and global influence.Combined with betweenness centrality,the entropy weight method is used to assign different weights to each index,and a multi-attribute decision-making hypernetwork important node identification method based on entropy theory is proposed.The advantages and disadvantages of different identification methods are compared through the natural connectivity of network and the maximum connectivity coefficient,and the empirical data of Xining city bus hypernetwork is used to further verify the effectiveness a feasibility of the proposed method.(2)Important node recognition in hypernetworks based on node propagation entropy.The propagation ability of a node depends on not only its local topology information,but also its global topology information.Based on hypergraph and information entropy theory,this paper uses node clustering coefficient and the number of neighbors to represent the local propagation influence of the node,and uses the shortest path between nodes and K-shell centrality to reflect the global propagation influence of the node,fully considering the influence of the node itself and its neighborhood nodes,and finally uses the node propagation entropy to represent the importance of the node in the network.Using monotonicity,robustness and SIR propagation model evaluation criteria,compared with other methods on six real networks from different fields,experimental results show that the proposed method can identify the important nodes in the hypernetwork accurately and effectively.(3)Important node recognition in weighted hypernetworks based on von Neumann entropy.With the in-depth study of hypernetworks,scholars find that the introduction of weights can more accurately reflect the internal relationship of real systems.Therefore,this paper takes the weighted hypernetworks as the research object,uses the idea of node deletion,calculates the von Neumann entropy of the weighted hypernetwork based on the eigenspectrum of the hyper-Laplacian matrix,and then discusses the recognition of the node importance in the weighted hypernetwork through the entropy difference.Finally,based on the network statistical characteristics,structural characteristics and transmission dynamics,the empirical analysis in the weighted hypernetwork of industry-university-research cooperation for invention patent application was carried out.The result shows that the proposed method is better than the methods of Hd andC_d~h.