cycle

A general cycle can be defined as a sequence of pairs of vertices and edges of finite length in which the edge in each pair connects the vertex of that pair to the vertex of the subsequent pair and the edge of the last pair connects to the vertex of the first pair. In general, cycles can have direction; that is the reverse of a cycle is a unique cycle.

For generality, it is not sufficient to use a sequence of vertices along since a pair of vertices can be connected by multiple edges. In order to define directionality, it is not sufficient to use a sequence of edges, because there are situations in which the starting vertex and direction of the cycle can be ambiguous.