edgetoorigin

Edgetoorigin is a term used to describe the origin endpoint of a directed edge in a graph. It identifies the vertex at which an edge begins, commonly called the source vertex or tail.

In formal terms, a directed graph G = (V,E) consists of vertices V and edges E, where each edge e ∈ E is an ordered pair (u,v). The edgetoorigin of e is u, while the destination is v.

Edges are stored as origin–destination pairs. In an adjacency list, an edge from u to v appears in the list for u; in an adjacency matrix, the entry at row u, column v indicates the edge.

Example: with vertices A,B,C and edges A→B, A→C, B→C, the origins are A for the first two edges and B for the third.

Applications include graph traversal (DFS, BFS), network modeling, and graph databases or visualization where the origin determines how data is linked and traversed. The out-degree of a vertex counts edges from that vertex; the in-degree counts edges to that vertex.

Note: some literature uses source vertex or tail instead of edgetoorigin. The term is descriptive and understood in the standard (origin, destination) edge representation.

See also: directed graph, vertex, edge, source vertex, tail, adjacency list, adjacency matrix.