Networks

• Introduction
• Construction of Networks
  • Network<n | edges >: RngIntElt, List → GrphNet, GrphVertSet, GrphEdgeSet
  • Network<S | edges >: SetEnum, List → GrphNet, GrphVertSet, GrphEdgeSet
  • Network<S | edges >: SetIndx, List → GrphNet, GrphVertSet, GrphEdgeSet
  • Example: GrphNet Constr
  • Magma Output: Printing of a Network
    • Example: GrphNet Constr2
• Standard Construction for Networks
  • Subgraphs
    • sub< N | list >: GrphNet, List → GrphNet, GrphVertSet, GrphEdgeSet
    • Example: Constr Sub Network
  • 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 > ] → GrphNet
    • N +:= < [ u, v ], c >: GrphNet, < [ GrphVert, GrphVert ], RngIntElt >
    • N +:= { < [ u, v ], c > }: GrphNet, {  < [ GrphVert, GrphVert ], RngIntElt > }
    • 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
    • AddEdges(N, S): GrphNet, [ < [  GrphVert, GrphVert ], RngIntElt > ] → GrphNet
    • AddEdge(~N, u, v, c): GrphNet, GrphVert, GrphVert, RngIntElt
    • AddEdge(~N, u, v, c, l): GrphNet, GrphVert, GrphVert, RngIntElt, .
    • AddEdges(~N, S): GrphNet, {  < [  GrphVert, GrphVert ], RngIntElt > }
    • AddEdges(~N, S): 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: Flow