HSC Mathematics Standard 2 topic guide

Networks

Networks is a core part of HSC Mathematics Standard 2. This guide connects the syllabus ideas behind Network Concepts, Critical Path Analysis, Network Flow, shows how they appear in worked problems, and points you to the formulas and full lessons needed for exam revision.

What you will learn

Networks syllabus outline

The units below follow the structure used in the full Study to Learn course. Use the outline to identify exactly which idea needs attention, then work through the public example before continuing to the complete lesson path.

E.1

Network Concepts

Network Diagrams and Shortest Paths

E.2

Critical Path Analysis

Activity Charts, Float Time and the Critical Path

E.3

Network Flow

Flow Networks & Terminology · Maximum Flow & Minimum Cut

Free worked preview

Network Diagrams and Shortest Paths

This complete preview comes from the Network Concepts unit. It introduces the core language, shows the method in context, and gives you a real example of the lesson quality before you create an account.

Networks, Revisited

A network consists of vertices connected by edges, often weighted (distance, time, or cost).

Key Terms

Degree: number of edges at a vertex. Path: a route along edges. Minimum spanning tree: the set of edges connecting all vertices with the smallest possible total weight, with no cycles.

Common ErrorThe shortest path between two specific vertices is not necessarily part of the minimum spanning tree (which connects ALL vertices as cheaply as possible) — these are two different, related but distinct problems.
Worked Example Find the shortest path from A to E, given edges: A-B(3), A-C(6), B-C(2), B-D(5), C-D(3), D-E(4).
1Route via B then DA-B-D-E:3+5+4=12\text{A-B-D-E}: 3+5+4=12
2Alternative route via B, C, then DA-B-C-D-E:3+2+3+4=12\text{A-B-C-D-E}: 3+2+3+4=12
3Route via C directlyA-C-D-E:6+3+4=13\text{A-C-D-E}: 6+3+4=13
Shortest total weight: 12 (two equally short paths found)\text{Shortest total weight: 12 (two equally short paths found)}
Practice QuestionGiven edges P-Q(4), P-R(9), Q-R(3), Q-S(7), R-S(2), find the shortest path from P to S.

Use the formulas

Keep the formula sheet beside you

Revision becomes faster when you practise locating the right equation and understand what every variable means. The full reference is public and searchable on any device.

Open HSC Mathematics Standard 2 Formula Sheet →

Reviewed by the Study to Learn editorial team · Updated 2026-07-24