MYP Extended Mathematics Network Types Notes

1. Graphs in graph theory are a powerful way to model connections in real life, such as rail routes, social interactions, or metro maps.
2. In this topic you will learn the main network types used in extended mathematics and how to recognize what each type can (and cannot) represent.

Graphs Model Connections Using Vertices And Edges

1. A graph (in graph theory) is made of vertices (points) and edges (connections between points).
2. This is a different meaning from the word "graph" used for plots on coordinate axes, so you must be careful with terminology.
3. Vertices are also commonly called nodes, and edges are also called arcs.

Order (Degree) Describes How Connected A Vertex Is

1. The order of a vertex (also called its degree) is the number of edges connected to it.
2. This is one of the simplest but most useful measurements in network problems:
   1. a high-order vertex may represent a major hub station in a metro system,
   2. a low-order vertex may represent an isolated location with few direct links.

Undirected Graphs Model Two-Way Relationships

1. In an undirected graph, an edge means the relationship works both ways.
2. This is appropriate when travel or connection is symmetric, for example:
   1. two people who can communicate (they share at least one common language),
   2. two stations joined by track that trains run in both directions,
   3. two computers connected by a cable where data can flow either way.

Connected And Disconnected Graphs Describe Reachability

1. A key property of an undirected graph is whether it is connected.
2. If a graph is not connected, it is disconnected, meaning it has at least two separate parts (components) with no path between them.