Graph Theory Modeling – A Petri Nets Based Approach

Abstract

There are many classic problems in graph theory which can be applied to research fields ranging from computer vision to transportation planning. Petri Nets (PNs) are mathematical objects which can be demonstrated by live graphic elements such as Place and Transition. They are competent in formalizing and solving issues in Graph theory. Take maximum flow problem as an example, though it has been well studied, its properties are rarely explored in the perspective of PNs to the best of our knowledge. In this paper, a Petri Nets based maximum flow modeling approach is proposed. Specifically, PN models of flow networks and the corresponding residual networks are firstly introduced. Based on the proposed models, the way of finding a maximum flow for a given flow network is presented. The PNs based maximum flow approach not only can solve the problem accurately, but also is intuitive and easy to understand resulting from its graphic simulation processes. Additionally, it is feasible to extent this work to other problems in graph theory as well.