  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.
