A cyclic edge cut of a connected graph is an edge cut such that at least two of the resulting connected components each contain at least one cycle. In a connected graph, each minimum cyclic edge cut splits the graph into exactly two components. In a disconnected graph with at least two components that each contain at least one cycle, the empty set of edges {} comprises a trivial cyclic edge cut (Dvořák et al. 2004). A cyclic edge cut of smallest possible size in a given graph is called a minimum cyclic edge cut. The cyclic edge cuts of two distinct types for the Petersen graph P are illustrated above. Each involves five edges, so the cyclic edge connectivity is λ_c(P) = 5.

cyclic edge connectivity | minimum cyclic edge cut