Kirchhoff's Circuit Law Applications to Graph Simplification in Search Problems

Abstract

This paper proposes a new analysis of graph using the concept of electric potential, and also proposes a graph simplification method based on this analysis. Suppose that each node in the weighted-graph has its respective potential value. Furthermore, suppose that the start and terminal nodes in graphs have maximum and zero potentials, respectively. When we let the level of each node be defined as the minimum number of edges/hops from the start node to the node, the proper potential of each level can be estimated based on geometric proportionality relationship. Based on the estimated potential for each level, we can re-design the graph for path-finding problems to be the electrical circuits, thus Kirchhoff's Circuit Law can be directed applicable for simplifying the graph for path-finding problems.• Kirchhoff's Current Law: KCL, also called Kirchhoff's first law, states that the sum of incoming currents at a junction is equal to the sum of outgoing currents at the junction. If we define the sign of incoming currents at the junction as positive and the sign of outgoing currents