Let G be a connected graph with V(G) = {1,⋯,n}. The shortest path distance d(i, j) between the vertices i, j 2 V(G) is the classical notion of distance and is extensively studied. However, this concept of distance is not always appropriate. Consider the following two graphs
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References and Further Reading
R.B. Bapat, Resistance distance in graphs, The Mathematics Student, 68:87–98 (1999).
R.B. Bapat, Resistance matrix of a weighted graph, MATCH Communications in Mathematical and in Computer Chemistry, 50:73–82 (2004).
B. Bollobás, Modern Graph Theory, Springer-Verlag, New York, 1998.
P.G. Doyle and J.L. Snell, Random Walks and Electrical Networks, Math. Assoc. Am., Washington, 1984.
D.J. Klein and M. Randić, Resistance distance, Journal of Mathematical Chemistry, 12:81–95 (1993).
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(2010). Resistance Distance. In: Graphs and Matrices. Universitext. Springer, London. https://doi.org/10.1007/978-1-84882-981-7_9
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