cycle,
n. 1. a permutation in which one subset of elements are moved cyclically and the remainder are not moved, such as
〈1, 2, 3, 4, 5〉 → 〈1, 4, 3, 2, 5〉.
If γ is a cycle that permutes exactly l elements, then l is the length of the cycle, and γ has order l, that is γl = e, where e is the identity permutation. Every permutation has a unique factorization as a product of disjoint cycles. See also alternating group, permutation. 2. a simple closed path in a graph.
〈1, 2, 3, 4, 5〉 → 〈1, 4, 3, 2, 5〉.
If γ is a cycle that permutes exactly l elements, then l is the length of the cycle, and γ has order l, that is γl = e, where e is the identity permutation. Every permutation has a unique factorization as a product of disjoint cycles. See also alternating group, permutation. 2. a simple closed path in a graph.