Solved at Scale
A Bigger Network
A real five-node, nine-arc network with exact integer capacities — including one pair of arcs running in both directions — parsed from the model file the external solver reads. No computation happens yet.
The instance
There are 5 nodes and 9 arcs with exact integer capacities, parsed from the solver's model file at build time, not hand-typed. Why: the earlier chapters' teaching network had 4 nodes and 5 edges; this one is the real instance the external solver reads.
Arcs both ways
One honest detail: arcs run both ways between N3 and N4 — one arc each direction, a normal feature of a real network. Why: nothing about max-flow forbids it, but it matters later, when this book's own teaching algorithm needs one small transformation to run on the same instance.
No computation yet
This lesson only presents the network. Why: the question is the usual one — how much flow can move from N1 to N5 — and the solving, with its certificate, comes next.
Diagram note
The table lists one row per arc, labeled by its endpoints — N1 to N5 style — with the exact capacity; those labels are the vocabulary this chapter uses everywhere. Pixel positions are rounded for layout; every number shown is exact.