For an undirected graph, an unordered pair of nodes that specify a line joining these two nodes are said to form an edge. For a directed graph, the edge is an ordered pair of nodes. 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 given classes on 
nodes.
| graph | OEIS |  , 2, ... |
| graph | A086314 | 0, 1, 6, 33, 170, 1170, 10962, 172844, 4944024, ... |
| labeled graph | A095351 | 0, 1, 12, 192, 5120, 245760, 22020096, ... |
| labeled tree | A053506 | 0, 1, 6, 48, 500, 6480, ... |
| planted tree | A055544 | 0, 1, 2, 6, 16, 45, 120, 336, 920, 2574, 7190, 20262, ... |
| rooted tree | A095350 | 0, 1, 4, 12, 36, 100, 288, 805, 2288, 6471, 18420, 52426, ... |
| tree | A095349 | 0, 1, 2, 6, 12, 30, 66, 161, 376, 954, 2350, 6061, 15612, 41067, ... |
See also
Edge Count, Graph Vertex, Hyperedge, Null Graph, Tait Coloring, Tait Cycle
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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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Cite this as:
Weisstein, Eric W. "Graph Edge." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GraphEdge.html