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This is a variation of the Shortest Path algorithm where not only the first one, but k-th shortest paths are returned
The Hoffman-Pavlet algorithm provides an implementation this problem for directed weight graph with positive weights.
IBidirectionalGraph<TVertex, TEdge> g = ...; Func<TEdge, double> edgeWeights = ...; TVertex source = ...; TVertex target = ...; int pathCount = 5; foreach(IEnumerable<TEdge> path in g.RankedShortestPathHoffman(g, edgeWeights, source, target, 5)) ...