# fn()fordFulkersonAlgorithmComputes a maximum flow in a directed graph.

Defined in ```TValue fordFulkeronAlgorithm(flow, g, source, sink, capacity); ```

## Parameters

 `flow` A property map with the flow of each edge. A directed graph. Types: Directed Graph A source vertex. Types: VertexDescriptor A sink vertex. Types: VertexDescriptor A property map of edge capacities.

## Return Values

`TValue` The value of the flow. TValue is the Value tpye of the type of flow.

## Detailed Description

### Example

```#include <iostream>
#include <seqan/graph_algorithms.h>

using namespace seqan;

int main()
{
typedef Graph<Directed<> > TGraph;
typedef VertexDescriptor<TGraph>::Type TVertexDescriptor;
typedef Iterator<TGraph, EdgeIterator>::Type TEdgeIterator;
typedef Size<TGraph>::Type TSize;

// Create graph with 10 directed edges (0,1), (0,4), ...
TSize numEdges = 10;
TVertexDescriptor edges[] = {0, 1, 0, 4, 1, 2, 1, 4, 2, 3, 2, 4, 4, 1, 4, 5, 5, 2, 5, 3};
TGraph g;
// Print graph.
std::cout << g << "\n";

// Create external property map for the edge capacities and assign to the graph.
String<unsigned int> capMap;
unsigned capacity[] =    {16, 13, 12, 10, 20, 9, 4, 14, 7, 4};
assignEdgeMap(capMap, g, capacity);

// Run the Ford-Fulkerson algorithm for maximum flow computation from source
// vertex 0 to sink vertex 3.  valF is the value of the flow.
String<unsigned int> flow;
unsigned valF = fordFulkersonAlgorithm(flow, g, 0, 3, capMap);

// Print the result to stdout.
std::cout << "Ford-Fulkerson (Value of the flow = " << valF << ")\n";
TEdgeIterator itEdge(g);
for (; !atEnd(itEdge); goNext(itEdge))
std::cout << "(" << sourceVertex(itEdge) << "," << targetVertex(itEdge) << "): "
<< "Flow: " << getProperty(flow, getValue(itEdge)) << ", Capacity: "
<< getProperty(capMap, getValue(itEdge)) << "\n";

return 0;
}
```
```Adjacency list:
0 -> 4,1,
1 -> 4,2,
2 -> 4,3,
3 ->
4 -> 5,1,
5 -> 3,2,
Edge list:
Source: 0,Target: 4 (Id: 1)
Source: 0,Target: 1 (Id: 0)
Source: 1,Target: 4 (Id: 3)
Source: 1,Target: 2 (Id: 2)
Source: 2,Target: 4 (Id: 5)
Source: 2,Target: 3 (Id: 4)
Source: 4,Target: 5 (Id: 7)
Source: 4,Target: 1 (Id: 6)
Source: 5,Target: 3 (Id: 9)
Source: 5,Target: 2 (Id: 8)

Ford-Fulkerson (Value of the flow = 23)
(0,4): Flow: 11, Capacity: 13
(0,1): Flow: 12, Capacity: 16
(1,4): Flow: 0, Capacity: 10
(1,2): Flow: 12, Capacity: 12
(2,4): Flow: 0, Capacity: 9
(2,3): Flow: 19, Capacity: 20
(4,5): Flow: 11, Capacity: 14
(4,1): Flow: 0, Capacity: 4
(5,3): Flow: 4, Capacity: 4
(5,2): Flow: 7, Capacity: 7
```

## Data Races

If not stated otherwise, concurrent invocation is not guaranteed to be thread-safe.