Multiple Edge (original) (raw)
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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 adirected multigraph.
See also
Graph Loop, Hypergraph, Königsberg Bridge Problem, Multigraph,Pseudograph
This entry contributed by Jonathan Vos Post (author's link)
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References
Grimaldi, R. P. Discrete and Combinatorial Mathematics: An Applied Introduction, 4th ed. Longman, 1998.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.
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Post, Jonathan Vos. "Multiple Edge." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/MultipleEdge.html