In this paper we propose a conductance electrical model to represent weighted undirected graphs that allows us to efficiently compute approximate graph isomorphism in large graphs. The model is built by transforming a graph into an electrical circuit. Edges in the graph become conductances in the electrical circuit. This model follows the laws of the electrical circuit theory and we can potentially use all the existing theory and tools of this field to derive other approximate techniques for graph matching. In the present work, we use the proposed circuital model to derive approximated graph isomorphism solutions.

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