The two definitions are equivalent in directed graphs, where simple cycles are also called "'directed cycles "': the cyclic sequence of vertices and edges in a walk is completely determined by the set of edges that it uses.
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"' Ideal ring bundle "'( IRB ) is a mathematical term which means an " n "-stage cyclic sequence of semi-measured terms, e . g . integers for which the set of all circular sums enumerates row of natural numbers by fixed times.
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It also considers : ( a ) systems considered in terms of cyclic sequences of processes rather than of states of the system; such were historically important in the conceptual development of the subject; and ( b ) systems considered in terms of processes described by steady flows; such are important in engineering.
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