Graph Edge

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, ...

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."