A new semi-local centrality for identifying influential nodes based on local average shortest path with extended neighborhood

Quantifying the importance of nodes in complex networks is known as the problem of identifying influential nodes and is considered a critical aspect in interacting with these networks. This problem has many applications such as controlling rumors, sickness spreading, and viral marketing, where its importance has been understood by the research society in the last decade. This paper proposes a new semi-local centrality to identify influential nodes in complex networks based on the theory of Local Average Shortest Path with extended Neighborhood concept (LASPN). LASPN focuses on a distributed technique to extract the subgraph associated with each node and apply the average shortest path theory to it. We use the extended neighborhood concept to find the nearest neighbors of each node with low complexity, where this can lead to high efficiency in dealing with large-scale networks. In addition to applying relative changes in the average shortest path, the proposed metric considers the importance of the node itself as well as its nearest neighbors in ranking the nodes. Evaluation of the proposed centrality metric has been done through numerical simulations on several real-world networks. The results based on Kendall's τ coefficient under the SIR infection spreading model show that LASPN improves the performance by 2.7