Editing Flow network (section)

=== Adding arcs and flows ===
{{Unreferenced section|date=June 2023}}
We do not use multiple arcs within a network because we can combine those arcs into a single arc. To combine two arcs into a single arc, we add their capacities and their flow values, and assign those to the new arc:
*Given any two nodes {{mvar|u}} and {{mvar|v}}, having two arcs from {{mvar|u}} to {{mvar|v}} with capacities {{math|''c''<sub>1</sub>(''u,v'')}} and {{math|''c''<sub>2</sub>(''u,v'')}} respectively is equivalent to considering only a single arc from {{mvar|u}} to {{mvar|v}} with a capacity equal to {{math|''c''<sub>1</sub>(''u,v'')+''c''<sub>2</sub>(''u,v'')}}.
*Given any two nodes {{mvar|u}} and {{mvar|v}}, having two arcs from {{mvar|u}} to {{mvar|v}} with pseudo-flows {{math|''f''<sub>1</sub>(''u,v'')}} and {{mvar|''f''<sub>2</sub>(''u,v'')}} respectively is equivalent to considering only a single arc from {{mvar|u}} to {{mvar|v}} with a pseudo-flow equal to {{math|''f''<sub>1</sub>(''u,v'')+''f''<sub>2</sub>(''u,v'')}}.
Along with the other constraints, the skew symmetry constraint must be remembered during this step to maintain the direction of the original pseudo-flow arc. Adding flow to an arc is the same as adding an arc with the capacity of zero.{{citation needed|date=February 2023}}