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.
Multiple Edge
See also
Graph Loop, Hypergraph, Königsberg Bridge Problem, Multigraph, PseudographThis 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.Referenced on Wolfram|Alpha
Multiple EdgeCite this as:
Post, Jonathan Vos. "Multiple Edge." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/MultipleEdge.html