• Mathematics General
  • Year 12

Graphs and Networks

approx. 11 hrs

11 topics

22 concepts

Develop a thorough understanding of Graphs and Networks to confidently solve a range of related problems.

Available in


In this area of study students explore graphs and networks and their use to model practical situations. Students will learn to identify different types of graphs and their features, including the application of Euler's formula. We will help students navigate a given network to determine the type of movement of each graph and solve a range of related problems.

Topics & Concepts We Cover

This learning program is made up of the following 11 topics, broken down into 22 concepts.

  • Network terminology 2 concepts

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

    2. Determine the degree of a vertex

  • Describing graphs 1 concept

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

  • Graphs and bridges 2 concepts

    1. Identify isomorphic graphs

    2. Identify connected graphs and bridges

  • Planar graphs 2 concepts

    1. Redraw a graph in planar form

    2. Identify planar graphs

  • Euler's formula 2 concepts

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

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

  • Adjacency Matrix 2 concepts

    1. Construct an adjacency matrix

    2. Construct a graph from an adjacency matrix

  • Movement around a graph 3 concepts

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

    2. Identify traversable graphs

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

  • Eulerian trails and circuits 3 concepts

    1. Investigate the Konigsberg bridge problem

    2. Identify eulerian trails and circuits

    3. Application of eulerian trails and circuits to contextual problems

  • Hamiltonian paths and cycles 2 concepts

    1. Identify hamiltonian paths and cycles

    2. Application of hamiltonian paths and cycles to contextual problems

  • Introduction to weighted graphs 1 concept

    1. Identify weighted graphs and networks

  • Shortest path including Dijkstra's algorithm 2 concepts

    1. Finding the shortest path through a network by inspection

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

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

Ready to start this program?

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Starting at

$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

Use anytime

Access to practice questions

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