MONOTONIC PATH ON NETWORK AND ITS APPLICATION TO THE CALCULATION OF TOTAL NUMBER OF PATHS BETWEEN TWO NODES

Abstract

The authors are interested in evaluating the connectivity of road networks in the event of a disaster such as a large-scale earthquake. It is impossible to predict the detailed damages caused by a large-scale earthquake in advance. In addition, there are various causes of road closure. This indicates that it is difficult to evaluate the connectivity using detailed data of damages. In this article, as an alternative, the authors propose a new method to the connectivity evaluation between two nodes based on the topology and geometry of a network. A network is firstly approximated as a merger of two independent tree structures from the two nodes assessed by Dijkstra’s method. The approximated network possesses a certain monotonicity. Then, a number of paths between the two nodes are calculated by the power of the adjacency matrix. A demonstrative example for the applicability of the proposed method is also presented.