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A graph edge of a simple graph is an unordered pair of distinct vertices specifying a connection between them. For a simple directed graph, the edge is an ordered pair of vertices. The terms "arc," "branch," "line," "link," and "1-simplex" are sometimes used instead of edge (e.g., Skiena 1990, p. 80; Harary 1994). Harary (1994) calls an edge of a graph a "line."

The following table lists the total number of edges in all graphs of the given classes on nodes. Unless labeled, the graphs are counted up to graph isomorphism. The graph rows use simple graphs.

See also

Directed Edge, Edge Count, Graph Face, Graph Vertex, Hyperedge, Null Graph, Tait Coloring, Tait Cycle, Undirected Edge

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References

Harary, F. Graph Theory. Reading, MA: Addison-Wesley, 1994.Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, 1990.Sloane, N. J. A. Sequences A053506, A055544, A086314, A095349, A095350, and A095351 in "The On-Line Encyclopedia of Integer Sequences."

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Graph Edge

Cite this as:

Weisstein, Eric W. "Graph Edge." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GraphEdge.html

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