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

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.

## Authors

• 2 publications
• 31 publications
• ### Minimum T-Joins and Signed-Circuit Covering

Let G be a graph and T be a vertex subset of G with even cardinality. A ...
03/09/2018 ∙ by Yezhou Wu, et al. ∙ 0

• ### Flooding edge or node weighted graphs

Reconstruction closings have all properties of a physical flooding of a ...
05/24/2013 ∙ by Fernand Meyer, et al. ∙ 0

• ### On Learning a Hidden Directed Graph with Path Queries

In this paper, we consider the problem of reconstructing a directed grap...
02/26/2020 ∙ by Mano Vikash Janardhanan, et al. ∙ 0

• ### A compact, structural analysis amenable, port-Hamiltonian circuit analysis

06/04/2020 ∙ by John D. Pryce, et al. ∙ 0

• ### Hand-Drawn Electrical Circuit Recognition using Object Detection and Node Recognition

With the recent developments in neural networks, there has been a resurg...
06/22/2021 ∙ by Rachala Rohith Reddy, et al. ∙ 0

• ### A* with Perfect Potentials

Quickly determining shortest paths in networks is an important ingredien...
10/28/2019 ∙ by Ben Strasser, et al. ∙ 0