Tunable path centrality: Quantifying the importance of paths in networks

•We propose a tunable path centrality based on local network structure.•We obtain the path centrality distribution on complex networks.•We apply the path centrality to the network fragility problem.

Centrality is a fundamental measure in network analysis. Specifically, centrality of a path describes the importance of the path with respect to the remaining part of the network. In this paper, we propose a tunable path centrality (TPC) measure, which quantifies the centrality of a path by integrating the path degree (PD) (number of neighbors of the path) and the path bridge (PB) (number of bridges in the path) with a control parameter ββ. Considering the complexity of large-scale and dynamical topologies of many real-world networks, both PD and PB are computed with only the local topological structure of a path. We demonstrate the distribution of the three path centralities (TPC, PD and PB) in computer-generated networks and real-world networks. Furthermore, we apply the three path centralities to the network fragility problem, and exploit the distribution of the optimal control parameter βoptβopt through simulation and analysis. Finally, the simulation results show that generally TPC is more efficient than PD and PB in the network fragility problem. These path centralities are also applicable in many other network problems including spread, control, prediction and so on.