Networks and Graph Theory in MYP Extended Maths
Explore graph theory networks in MYP Extended Maths Year 5. Learn nodes, edges, Eulerian paths, and spanning trees for Criterion B investigations and Criterion D tasks.
Graph Theory, Not Computer Networks
In MYP Extended Mathematics, "networks" refers to graph theory — a branch of mathematics dealing with nodes (vertices) and edges (connections). This is not about internet or computer networks. Graph theory provides tools to model and solve problems involving routes, connections, and relationships between objects.
Key Vocabulary
- Node (vertex): a point representing an object or location.
- Edge: a line connecting two nodes, representing a relationship or route.
- Degree of a node: the number of edges connected to it.
- Path: a route through the network that visits each edge or node.
- Connected graph: a graph where every node can be reached from every other node.
- Weighted graph: a graph where each edge has a numerical value (distance, cost, time).
Types of Problems
Traversability
An Eulerian path visits every edge exactly once. This is possible if and only if the graph has exactly zero or two nodes of odd degree. An Eulerian circuit (returning to the start) requires all nodes to have even degree. These are classic Criterion B investigation starting points — you can conjecture the rule from examples and then verify it.
Shortest Path
In a weighted network, finding the shortest path between two nodes is a practical optimisation problem. At MYP level this is typically done by systematic inspection or a simple algorithm rather than formal Dijkstra's algorithm.
Spanning Trees
A minimum spanning tree connects all nodes using the fewest edges and minimum total weight. This concept appears in logistics and design contexts — natural Criterion D material.
MYP Assessment Context
Networks problems at Extended level are well-suited to Criterion B (investigating patterns — for example, conjecturing the rule for Eulerian paths from a set of graphs) and Criterion D (applying a network model to a real situation such as planning delivery routes or designing a communication system). Criterion C marks come from precise use of graph theory vocabulary in your explanations.
Common Mistakes
- Confusing degree with the number of nodes — degree is the count of edges at a single node.
- Attempting to draw an Eulerian path on a graph with four odd-degree nodes without checking feasibility first.
- Using informal language like "connections" instead of precise terms like edges and nodes in written responses.