IB Math AI AHL 3.15 - Adjacency Matrices Notes

IB Maths AI HL 3.15 Notes – Adjacency Matrices

This IB Maths AI HL 3.15 resource introduces adjacency matrices and their use in analysing graphs and networks, and is fully aligned with the IB Applications and Interpretation HL syllabus.

Students learn how graphs can be represented using matrices, where each entry in an adjacency matrix indicates whether a connection exists between two vertices. The notes explain how this representation allows networks to be studied using matrix operations and how the interpretation changes for directed graphs where the order of vertices matters.

The resource develops the concept of walks in a graph and explains how the length of a walk corresponds to the number of edges used. A key result is introduced: powers of the adjacency matrix can be used to count the number of walks of a given length between two vertices. Students learn how to compute matrix powers and interpret entries in (A^k) to determine the number of possible routes in a network.

Structured practice problems guide students through constructing adjacency matrices for networks, interpreting matrix powers, and identifying routes between locations in both undirected and directed graphs. The notes also introduce weighted adjacency tables and transition matrices, linking graph theory with probability models used later in the course.

Ideal for IB Maths AI HL teachers teaching adjacency matrices, walks in graphs, and the connection between graph theory and matrix methods.