Identify important nodes by local betweenness centrality-based entropy for graph signals

Due to the rapid development of complex networks in various disciplines, identifying important nodes in networks has become a particularly prominent issue. Classical local methods generally only consider the nodes neighboring a given node, without taking into account the information contained between them. To study the influence of local neighbor nodes more deeply, this paper proposes a node importance method based on the product of graph signals. First, the betweenness centrality of each node and the difference between neighboring nodes is calculated. Then, appropriate networks are constructed and information is mapped onto them using graph signals. Finally, the entropy value of the newly proposed entropy is calculated using the Kronecker product of the graph. This method considers not only the relationship between a node and its neighbors but also the relationships between neighboring nodes, providing a clearer description of node importance. Experimental results demonstrate that Local Betweenness Centrality-based Entropy performs well on classical and real-world networks.