Identify influential nodes in directed networks: A neighborhood entropy-based method

The identification of influential nodes in complex networks is prominent and actively researched topic, with applications across various fields. Despite the emergence of numerous methods, many of these are inadequate for directed networks due to the asymmetry of information flow. To address this challenge, we propose a Neighborhood Entropy-based Method (NEM) for identifying key nodes in directed networks. Inspired by Shannon entropy, the k-orders in-degree entropy and k-orders out-degree entropy of nodes are defined to capture the neighborhood information of the node. A tunable parameter α is introduced to balance the contribution of in-neighbors and out-neighbors on neighbor influence ability, while a decay factor φk is set to adjust the influence of different order neighbors on the node. The importance of a node can be eventually evaluated by the influence capability of its in-neighbors and itself. To assess the effectiveness of NEM, we benchmark it against six existing methods on six real network datasets. The results demonstrate the high correctness of NEM, with its low time complexity enabling efficient application to large-scale directed networks.