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# max_flow_with_lb(+Graph, +LowerBoundArg, +CapacityArg, +SourceNode, +SinkNode, -MaxFlowValue, -MaxFlowEdges, -MaxFlowEdgesGraph)

Finds rhe maximum flow for a network with non-negative lower-bounds imposed on the edge flows,using an adapted Ford-Fulkerson maximum flow algorithm
*Graph*
- a graph structure, no parallel edges, e(Src,Dest,EdgeData)
*LowerBoundArg*
- which argument of EdgeData to use as the minimum flow (lower bound) for edge (integer)
*CapacityArg*
- which argument of EdgeData to use as edge capacity (integer),
*SourceNode*
- source node number (integer)
*SinkNode*
- sink node number (integer)
*MaxFlowValue*
- value of the maximum flow
*MaxFlowEdges*
- list denoting edges with non-zero flow (form: Flow-Edge)
*MaxFlowEdgesGraph*
- a graph structure, original nodes (as in Graph) but only the edges that are in max flow

## Description

This predicate provides an implementation of the Ford-Fulkerson max-flow algorithm between two nodes in a graph, modified to allow edges to have non-negative minimum flows. It returns the maximal achievable flow allowed by the capacities in the network, a list of all edges with non-zero flow, and a graph of the edges with non-zero flow.
### Fail Conditions

There is no feasible flow between Source and Sink nodes.
## See Also

max_flow_with_lb / 6, max_flow / 5, max_flow / 7, feas_flow_with_lb / 8, all_min_cuts : all_min_cuts / 8, all_min_cuts : all_min_cuts / 9, all_min_cuts : all_min_cuts_list / 5