Multiple Edge

Multiple edges are two or more edges connecting the same two vertices within a multigraph. Multiple edges of degree  between vertex  and vertex  correspond to an integer  as the  entry of the incidence matrix of the multigraph. A diagonal entry  corresponds to a single or multiple loop. Integers  can similarly correspond to multiple edges in a directed multigraph.

REFERENCES

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Gross, J. T. and Yellen, J. Graph Theory and Its Applications. Boca Raton, FL: CRC Press, 1999.

Harary, F. Graph Theory. Reading, MA: Addison-Wesley, p. 10, 1994.

Hartsfield, N. and Ringel, G. Pearls in Graph Theory: A Comprehensive Introduction, 2nd ed. San Diego, CA: Academic Press, 1994.

Pemmaraju, S. and Skiena, S. Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Cambridge, England: Cambridge University Press, 2003.

Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, 1990.

Tutte, W. T. Graph Theory as I Have Known It. Oxford, England: Oxford University Press, 1998.

West, D. B. Introduction to Graph Theory, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 2000.Zwillinger, D. (Ed.). CRC Standard Mathematical Tables and Formulae, 31st ed. Boca Raton, FL: CRC Press, 2003.