Cocycle

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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.

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Let G be a graph with vertex set V. A cut is a partition 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]