Introducing a networks resiliency measuring index in the disaster situation by using developed minimum spanning tree concept

The network's proper functioning is directly related to the amount of access and the ability to communicate with various activities. If a network, even during regular operation, is desirable and acceptable, its desirable performance cannot be extended to the post-crisis situation for its various reasons. Therefore, one of the principal methods for preventing damage to the transportation network and proper management of various disasters, including earthquakes, is to study the decline in the transportation network's performance. One of the critical characteristics of a network can be the minimum spanning tree problem. As network links connectivity is close to the tree, the network would be more vulnerable to disaster situations. In this study, using the minimum spanning tree concept, we investigate the transportation network’s evolution in crises. The results show that a large proportion of the arterial roads of each province are located in the minimum spanning tree of that province; so, as an example, in the province of Tehran, as the capital of the country, the ratio of the links in the minimum spanning tree comprises a total of links is equal to 73%. The ratio of the length of the province's links, which is included in the minimum spanning tree, is 78%. The results show that a large part of the country's arterial roads' network needs careful planning and improvement before any crises occur.