Graph Terminology

Graph G = (V, E) is a set of vertices V, with set of edges E.

Directed

Edges which have a specific direction associated with them so that each edge can be traversed in one direction only.

Undirected

edges do not have a direction associated so that each edge can be traversed in each direction.

Path

The set of edges and vertices which connect one vertex to another vertex.

Connected

Two vertices which are connected via a valid path.

Strongly Connected

Connected in more than one path, such that no single vertex or single path can be remove and make the graph unconnected.

Degree

Equals the number of edges going out/in from/to a single vertex.

Cycle

A path within a graph which can loop back to an ancestor node/vertex.

Tree

A graph which contains no cycles.