A New Framework for Solving the Spatial Network Problems Based on Line Graphs

In this article we define inverse line graphs of directed graphs as a new framework for solving some classical network analysis problems. The extraction method and theories of inverse line graphs are explained in this article. It is shown that by changing the analysis space from the original directed graph to the inverse line graph, complex problems can be changed into simpler problems. We show the usefulness of the proposed framework in two particular applications: shortest path computations and the more general route planning. Considering the implementation result, we expect that this framework could be used in many more network analysis problems.