Abstract
In this study, we propose novel centrality measures considering multiple perspectives of nodes or node groups based on the facility location problem on a spatial network. The conventional centrality exclusively quantifies the global properties of each node in a network such as closeness and betweenness, and extracts nodes with high scores as important nodes. In the context of facility placement on a network, it is desirable to place facilities at nodes with high accessibility from residents, that is, nodes with a high score in closeness centrality. It is natural to think that such a property of a node changes when the situation changes. For example, in a situation where there are no existing facilities, it is expected that the demand of residents will be satisfied by opening a new facility at the node with the highest accessibility, however, in a situation where there exist some facilities, it is necessary to open a new facility some distance from the existing facilities. Furthermore, it is natural to consider that the concept of closeness differs depending on the relationship with existing facilities, cooperative relationships and competitive relationships. Therefore, we extend a concept of centrality so as to considers the situation where one or more nodes have already been selected belonging to one of some groups. In this study, we propose two measures based on closeness centrality and betweenness centrality as behavior models of people on a spatial network. From our experimental evaluations using actual urban street network data, we confirm that the proposed method, which introduces the viewpoints of each group, shows that there is a difference in the important nodes of each group viewpoint, and that the new store location can be predicted more accurately.
Highlights
In recent years, networks have been widely observed around us, and the technology of network science has been applied to various real-world problems
When adding a new node to a group based on the concept of group centrality, it is natural to select the node that can raise the group centrality score most. This is equivalent to the greedy solution method for the combinatorial optimization problem that finds the combination of nodes so as to maximizes the group centrality score
We proposed a new measure based on betweenness centrality, i.e., in the conference paper, we only proposed and evaluated closeness centrality based measure
Summary
Networks have been widely observed around us, and the technology of network science has been applied to various real-world problems. To the best of our knowledge, this is the first study that considers such cooperative and competitive relationships to analyze a road network and applies it to facility location issues As another stream of centrality research, modular centrality has been developed in recent years, which is an extended version of classical centrality measures in terms of two perspectives, local and global (Ghalmane et al 2019a, b; Cherifi et al 2019). The most classical stream of studies includes p-center or p-median problems, where demand points (residents, customers) select the closest facility by physical distance In this assumption, the most simple way to estimate shares is the proximity approach (Hotelling 1929), the idea of which is equal to our closeness based model. We call the methods that extract a node according to Eq 5 based on closeness and betweenness models to Multiple Perspective CLoseness Centrality (MPCLC) and Multiple Perspective BetWeenness Centrality (MPBWC), respectively
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