Multiple edges, also called parallel edges, are two or more graph edges connecting the same two graph vertices
within a multigraph. For distinct graph
vertices 
and 
, the 
entry 
of the adjacency matrix
records the number of graph edges joining them, so
multiple edges give 
.
Diagonal entries record loops, with conventions differing
on whether each graph loop contributes one or two.
In a directed graph, 
records the number of directed graph
edges from 
to 
.
Multiple Edge
See also
Graph Loop, Hypergraph, Königsberg Bridge Problem, Multigraph, PseudographPortions of this entry contributed by Jonathan Vos Post
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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:
Weisstein, Eric W., with contributions by Jonathan Vos Post. "Multiple Edge." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MultipleEdge.html
