• Mathematics General
  • Year 12

Graphs and Networks

approx. 14 hrs

2 topics

41 concepts

Develop extensive understanding of Graphs and Networks and the skills for examination success.

Available in


The Graphs and Networks program is an essential part of the Year 12 Mathematics General course as outlined in the Australian curriculum. We show students how to use graphs and networks to represent and analyse everyday situations. They conduct analysis on information contained in graphs and networks and communicate conclusions using appropriate mathematical language, notation and diagrams.

Topics & Concepts We Cover

This learning program is made up of the following 2 topics, broken down into 41 concepts.

  • Graph theory 9 concepts

    1. Using Euler's formula to determine element values of a connected planar graph

    2. Identify planar graphs

    3. Redraw a graph in planar form

    4. Construct a graph from an adjacency matrix

    5. Construct an adjacency matrix

    6. Determine the degree of a vertex

    7. Identify elements of a graph including dots, vertices, edges, loops and faces

    8. Verify Euler's rule given a connected planar graph

    9. Identify connected graphs and bridges

  • Application of Graph Theory 32 concepts

    1. Draw directed and weighted bipartite graphs

    2. Determine the maximum flow for any section of sequential edges of a directed graph

    3. Use crashing to reduce the completion time of a project

    4. Use the Hungarian algorithm to determine an optimum allocation in order to minimise cost

    5. Identify isomorphic graphs

    6. Determine the float time for activities in an activity network

    7. Determine the critical path for an activity network

    8. Determine the overall minimum completion time for a project using critical path analysis

    9. Use forward scanning to determine the earliest starting time of activities in an activity network

    10. Reading a graph to write down the list of vertices in order of a walk, trail, path, circuit or cycle

    11. Use backward scanning to determine the latest starting time of activities in an activity network

    12. Write down a precedence table or activity chart from an activity network

    13. Create an activity network from a precedence table or activity chart

    14. Decide when to use dummy activities in an activity network

    15. Determine the maximum flow as equal to the minimum cut capacity

    16. Describe the flow of material through a directed graph

    17. Determine cut capacities

    18. Define and describe a directed graph (digraph)

    19. Application of eulerian trails and circuits to contextual problems

    20. Identify eulerian trails and circuits

    21. Determine the shortest path through a directed graph using Dijkstra's algorithm

    22. Identify hamiltonian paths and cycles

    23. Application of hamiltonian paths and cycles to contextual problems

    24. Identify weighted graphs and networks

    25. Identify traversable graphs

    26. Identify and describe the movement around a graph as a walk, trail, path, circuit or cycle

    27. Use Prim's algorithm to obtain a minimum spanning tree

    28. Solving connector problems

    29. Identify tree structures from a graph including spanning trees

    30. Finding the shortest path through a network by inspection

    31. Finding the shortest path through a network by Dijkstra's algorithm

    32. Demonstrate the meaning of, and use, the terms: subgraph, simple graph, complete graph, bipartite graph, digraph, arc, weighted graph and network

What you'll get

Learning Content

  • A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
  • All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions

An Expert Tutor

  • We match you to a private, expert tutor who is right for your needs and goals
  • Our tutors are talented, tested, top ATAR achievers and subject experts
  • During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in Graphs and Networks


  • Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
  • You and your parents receive a comprehensive feedback report after every session
  • Every session is recorded and available for you to watch at any time, allowing you to review what was covered

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Starting at

$49(inc. GST)

per session

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Access to practice questions

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