Graph A graph is denoted as with nodes or vertices $V$, and edges $E$. Edge An edge is a pair of nodes $u, v \in V$. The pair is ordered $e = (u, v) \in E$ when $G$ is directed. It is unordered when is undirected.
Unless otherwise stated, definitions apply to either directed or undirected graphs (with slight modifications).
Neighbor A node is a neighbor of a node exactly when , that is when and are connected by an edge. The set of neighbors of a node is denoted as
or for sake of simplicity.
Path A path is a sequence of edges that shares endpoints
with , .
Cycle / Circuit When the start and end node of a path coincide, , the path is called a cycle. When is directed, the name circuit is sometimes preferred.