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.
| 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, ... |
