Year 12: Networks

6 dot points across 6 inquiry questions, in syllabus order. Each dot point has a focused answer, with exam-style questions and worked answers where available.

What is the critical path in a project network, and how does it determine the minimum project duration?

Construct an activity network from a precedence table, identify the critical path and find the minimum project duration

Critical path analysis. Building an activity network from a precedence table, identifying paths through the network, and determining the minimum project duration via the critical (longest) path with worked Australian construction examples.

15 min read →

What are the basic terms and components of a network, and how are real-world systems represented as graphs?

Use network terminology including vertex, edge, weight, degree, path, cycle and directed graph to describe and analyse networks

Network terminology. Vertices, edges, weights, degree and the handshake result, walks, paths and cycles, connected graphs, trees and the n minus 1 edges fact, traversability with the even-degree test for Eulerian trails, and worked Australian examples for transport networks and project schedules.

15 min read →

How is the greatest possible flow through a directed network found, and why does the smallest cut decide it?

Solve network flow problems, including finding the maximum flow using the maximum-flow minimum-cut theorem

Network flow. Sources and sinks, edge capacities, saturated edges, finding the maximum flow by inspection, cuts and cut capacity, the maximum-flow minimum-cut theorem, and multiple sources or sinks via a super-source and super-sink, with worked water, traffic and data examples.

16 min read →

What is a minimum spanning tree, and how is it found using Prim's or Kruskal's algorithm?

Find a minimum spanning tree for a weighted graph using Prim's or Kruskal's algorithm

Minimum spanning trees. Definition of a spanning tree and minimum spanning tree, step-by-step Prim's and Kruskal's algorithms, and worked examples for utility networks and rural Australian infrastructure planning.

12 min read →

How do forward and backward scanning give the earliest and latest start times of each activity, and how is float calculated?

Perform forward and backward scanning to find earliest start, latest start, earliest finish, latest finish times and float for each activity

Forward and backward scanning. Computing earliest start, latest start, earliest finish, latest finish and float for each activity in a project network, with worked Australian construction and renovation examples.

16 min read →

How is the shortest path between two vertices in a weighted network found?

Find the shortest path between two vertices in a weighted network by inspection or by systematic labelling

Shortest paths. Inspection for small networks, systematic labelling (Dijkstra-style) for larger ones, a stage-by-stage walkthrough, ties and verification edge cases, and worked road and Sydney transport examples.

14 min read →