CWIIIF: A Novel Algorithm for Identifying Influential Nodes in Multilayer Networks

The identification of influential nodes in multilayer networks is a rapidly growing area in network science. However, insufficient consideration of both inter- and intra-layer weights in existing research has limited the effectiveness of node identification methods. To address this gap, we propose a novel algorithm, coupling weighted intra-layer and inter-layer influence factors (CWIIIF), which accurately identifies nodes that exert significant influence in multilayer networks. The algorithm integrates weighted intra- and inter-layer influence factors, taking into account the unique properties of multilayer network structures. First, we define a set of layer weight influence parameters, including active nodes, active paths, and communication intersections between layers, to determine the weight of each network layer. We then calculate the intra-layer influence of each node using a combination of K-shell and betweenness centrality methods. Finally, we introduce a set of coupled equations that convert the intra-layer influence vectors into scalar values by incorporating the weights of each layer, producing a final influence score for each node. To validate the effectiveness of our algorithm, we conducted four comparative experiments across nine real-world and one synthetic multilayer networks. The results demonstrate that our algorithm significantly outperforms nine classical and state-of-the-art methods for identifying influential nodes.