Network Concepts
Network Diagrams & Terminology · Shortest Path Problems
HSC Mathematics Standard 1 topic guide
Networks
Networks is a core part of HSC Mathematics Standard 1. This guide connects the syllabus ideas behind Network Concepts, 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.
Free worked preview
Network Diagrams & Terminology
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
A network (or graph) is a diagram of vertices (points, representing locations/items) connected by edges (lines, representing connections/routes), often labelled with a weight (e.g. distance, cost, time).
Key Terms
- Degree of a vertex: the number of edges connected to it
- Path: a route through the network, moving along edges from vertex to vertex
- Connected network: every vertex can be reached from every other vertex, via some path
Common ErrorThe degree of a vertex counts every edge connected to it, including any edges that appear to cross others elsewhere in the diagram (crossings don't create a vertex unless explicitly marked as one) — only actual vertices matter.
Worked Example
A network has vertices A, B, C, D. Edges: A-B, A-C, B-C, B-D, C-D. Find the degree of each vertex.
1Count edges touching A
2Count edges touching B
3Count edges touching C and D similarly
Practice QuestionDraw a network with 4 towns where each town is directly connected to exactly 2 others, forming a single loop. What is the degree of every vertex?
Reviewed by the Study to Learn editorial team · Updated 2026-07-24