Graphs and Matrices pp 111-124 | Cite as

# Resistance Distance

Chapter

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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Random Walk Span Tree Connected Graph Minimum Norm Classical Distance
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## References and Further Reading

- 1.R.B. Bapat, Resistance distance in graphs, The Mathematics Student, 68:87–98 (1999).MathSciNetGoogle Scholar
- 2.R.B. Bapat, Resistance matrix of a weighted graph, MATCH Communications in Mathematical and in Computer Chemistry, 50:73–82 (2004).MathSciNetzbMATHGoogle Scholar
- 3.B. Bollobás, Modern Graph Theory, Springer-Verlag, New York, 1998.zbMATHGoogle Scholar
- 4.P.G. Doyle and J.L. Snell, Random Walks and Electrical Networks, Math. Assoc. Am., Washington, 1984.Google Scholar
- 5.D.J. Klein and M. Randić, Resistance distance, Journal of Mathematical Chemistry, 12:81–95 (1993).CrossRefMathSciNetGoogle Scholar

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