Cyclicity#
Definition: Cycle
A cycle in a directed multigraph is a walk
\[ (v_0, e_1, v_1, e_2, v_2, \dotsc, e_k, v_k) \]
of length \(k \ge 1\) such that \(v_0 = v_k\) and \(v_i \ne v_j\) for all distinct \(i, j \in \{0, \dotsc, k-1\}\).
Definition: Cyclicity
A directed multigraph is cyclic if it contains at least one cycle and is acyclic otherwise.