HSC · Mathematics Standard 2 · Networks · also VCE Networks & Decision Maths live from the app

Network Flow and the Maximum-Flow Minimum-Cut Theorem

How much can a network carry? Pipes, roads and data links all obey the same law: the maximum flow through a network equals the capacity of its tightest cut. Find the bottleneck and you have found the answer. This is the real knowscape from knowhere, not a picture of one. Drag it. Watch what actually changes.

mathematics standard 2 · networks · network flow and the maximum-flow minimum-cut theoremdrag it · it is yours
the one idea

why this one carries the topic.

A network is a diagram that turns a real system — roads, pipes, cables, schedules — into dots and weighted lines, and every question is about optimising one thing along those lines. Either you connect everything for the least total cost (spanning tree) or you push the most through a fixed structure (flow). The bottleneck is always the answer.

The maximum flow through a network from source to sink equals the minimum capacity of any cut that separates source from sink, meaning the bottleneck determines total throughput.

what examiners catch — Students often forget to check all possible cuts systematically or incorrectly identify cuts by only looking at obvious bottlenecks rather than calculating capacity sums for every source-sink partition.
what you leave with

five things, not forty.

what's underneath

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knowhere maps every concept to what it rests on and what rests on it — 1 underneath this one, 0 built on top. Each one says why, in a sentence, not as an arrow on a diagram.

this conceptnetwork flow and the maximum-flow minimum-cut theoremThe maximum flow through a network from source to sink equals the minimum capacity of any cut that separates source from sink, meaning the bottleneck determines total throughput.
sits under itnetwork components and terminologybecause source, sink and cut are network terminology
the rest of networks

3 more, same treatment.

Each one is its own knowscape in the app — built for how a particular student takes things in, not one explanation handed to everybody.

network flow and critical path analysisin the appminimum spanning treesin the appproject scheduling and critical pathin the app
this is one of 865

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knowherehsc mathematics standard 2network flow and the maximum-flow minimum-cut theorem