This graph maintains the invariant that it is free of such cycles that the total length of edges involving is negative. With introduction of those negative-cycles causes an inability to compute the shortest paths from arbitrary vertex. By using the graph modules defined here, introduction of such a cycle is automatically prevented.

`module Imperative (G : Sig.IM) (W : Sig.WEIGHT with type edge = G.E.t) : sig ... end`
`module Persistent (G : Sig.P) (W : Sig.WEIGHT with type edge = G.E.t) : sig ... end`

Persistent graphs with negative-cycle prevention