Introduction

 
Construction of Networks
      Network<n | edges > : RngIntElt, List -> GrphNet, GrphVertSet, GrphEdgeSet
      Example Network_GrphNet_Constr (H164E1)

      Magma Output: Printing of a Network
            Example Network_GrphNet_Constr2 (H164E2)

 
Standard Construction for Networks

      Subgraphs
            sub< N | list > : GrphNet, List -> GrphNet, GrphVertSet, GrphEdgeSet
            Example Network_ConstrSubNetwork (H164E3)

      Incremental Construction: Adding Edges
            N + < [ u, v ], c > : GrphNet, < [ GrphVert, GrphVert ], RngIntElt > -> GrphNet, GrphEdge
            N + { < [ u, v ], c > } : GrphNet, { < [ GrphVert, GrphVert ], RngIntElt > } -> GrphNet
            N +:= < [ u, v ], c > : GrphNet, < [ GrphVert, GrphVert ], RngIntElt > ->
            AddEdge(N, u, v, c) : GrphNet, GrphVert, GrphVert, RngIntElt -> GrphNet, GrphEdge
            AddEdge(N, u, v, c, l) : GrphNet,GrphVert, GrphVert, RngIntElt, . -> GrphNet, GrphEdge
            AddEdges(N, S) : GrphNet, { < [ GrphVert, GrphVert ], RngIntElt > } -> GrphNet
            AddEdge(~N, u, v, c) : GrphNet, GrphVert, GrphVert, RngIntElt ->

      Union of Networks

 
Maximum Flow and Minimum Cut
      MinimumCut(s, t : parameters) : GrphVert, GrphVert -> SeqEnum, RngIntElt
      MinimumCut(Ss, Ts : parameters) : [ GrphVert ], [ GrphVert ] -> SeqEnum, RngIntElt
      MaximumFlow(s, t : parameters) : GrphVert, GrphVert -> RngIntElt, SeqEnum
      MaximumFlow(Ss, Ts : parameters) : [ GrphVert ], [ GrphVert ] -> RngIntElt, SeqEnum
      Flow(e) : GrphEdge -> RngIntElt
      Flow(u, v) : GrphVert, GrphVert -> RngIntElt
      Example Network_Flow (H164E4)

 
Bibliography

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