COCYCLE

A 'cocycle' refers to any one of the following:

★ A closed cochain in algebraic topology is called a cocycle.

★ A particular type of map in an autonomous dynamical system; see Oseledec theorem.

Let G by a graph with vertex set V. A cut is a partition of S = {X, X'} of V into two nonempty subsets. We denote the set of all edges incident with one vertex in X and one vertex in X' by E(S) or E(X, X'); and any such edge set is called a 'cocycle'. [pg 103 ISBN 1431-1550]