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A cycle cover of a finite directed graph is a collection of vertex-disjoint directed cycles containing every vertex exactly once. Cycle covers of the weighted directed graph with adjacency matrix $A$ are the terms in the permanent of a matrix $\mathrm{perm}A$.

This is a vertex cycle cover with the additional requirements of directed cycles and vertex disjointness.

A vertex cycle cover is a collection of cycles whose union contains every vertex of a graph; its cycles can overlap. A cycle cover of a directed graph additionally requires directed, vertex-disjoint cycles, and a spanning circuit family can allow overlaps.