A New Group Centrality Measure for Maximizing the Connectedness of Network Under Uncertain Connectivity

Abstract

In this paper, we propose a new centrality measure for the purpose of estimating and recommending installation sites of evacuation facilities that many residents can reach even in the situation where roads are blocked by natural disasters. In the proposed centrality, we model the probabilistically occurring road blockage by the link cut of the graph, and quantify the degree of connectivity of each node by the expectation value of the number of reachable nodes under uncertain connectivity. In a large-scale network, since the number of combinations of disconnecting links is enormous, it is difficult to strictly calculate the expected value. Therefore, approximate connectivity is calculated by an efficient algorithm based on simulation. Furthermore, in order to estimate multiple installation sites, we propose a method of defining and maximizing the degree of connectivity for a node group rather than a single node. From this, it can be expected that duplication of nodes covered by the extracted nodes can be eliminated, so that a practical candidate site of evacuation facility can be estimated. We evaluate the effectiveness and efficiency of the proposed method compared with the method based on distance between nodes and the method based on link density, using real road networks.