A location centrality of nodes in complex networks

The nodes’ centrality is a powerful tool built for the quantification of nodes’ influence on the whole network. However, most of the existing nodes’ centrality is defined from the topological structure of nodes, ignoring the relative position information. In this work, the location centrality of nodes is proposed to quantify the nodes’ influence from the spatial distribution and relative position of nodes in a network, which is independent of their functional status. Location centrality is a revelation of the intrinsic structure and position information of complex networks, which also avoids the difficulty of defining and finding the network center that generally exists in traditional location-based centrality. It also has relatively lower computational complexity. Through network attack experiments, we have validated that location centrality has a high sensitivity on the nodes’ locational data. We also introduced the V-index to assess the impact of centrality metrics on attacks, and we found that the positional centrality’s V-index consistently can serve as a reliable criterion to show the network’s generative mechanisms. We also found that the distribution of location centrality fits the power law distribution. Those results show that location centrality is a new position-based network analysis method, and it can offer special insights for us to understand the structure of complex networks.