# 2.5 Networks

## AS 91260

### General Information

Networks (AS 91260) is a 2 credit internal.

Networks is a small and very visual topic at Level 2. It can lead to Critical Path Analysis at Level 3.

### Overview

Networks can be used to represent many different real-world situations, everything from road networks, to airline routes, to connections on social media, to biological systems.

To get started with networks, it is helpful to know some basic terminology: node (vertex), edge (arc), tree, cycle, path.

Overview Starter

Notes (Word) (PDF)

Workbook References: NuLake IAS 2.5 pg (3) 4

Introduction to Networks

The Seven Bridges of Königsberg (Maths is fun | nrich)

### Traversability

What is traversability? How can we tell if a newtwork is traversable? Can you justify why a network is traversable? Can you modeify a network that isn't traversable to make it traversable?

Traversability Starter

Traversability Notes (Word) (PDF)

Workbook References: NuLake IAS 2.5 pg (5,6) 7,8 pg (9) 10,11 pg (12) 13,14,15,16

### Shortest Path

Shortest path is exactly what it sounds like: the shortest route between two nodes.

Shortest Path Starter

Shortest Path Notes (Word) (PDF)

Workbook References: NuLake IAS 2.5 pg (26) 27, 28, 29, 30, 31, 32, 33, 34

### Minimum Spanning Tree

Minimum Spanning Trees have many proactical uses, from creating a fibre optic network, to a creating a water network for a city.

Several algorithms exist for finding minimum spanning trees, including Prim's and Kruskal's algorithms. However, we find the easiest to be the Reverse-Delete algorithm.

Minimum Spanning Tree Starter

Minimum Spanning Tree Notes (Word) (PDF)

Workbook References: NuLake IAS 2.5 pg (35,36,37,38,39) 40,41, 42

### Table to Network

One of the easiest ways to specify a network is by using a table. From the table, a network will need to be constructed to solve problems involving traversability etc.

Network From Table Starter

Network From Table Notes (Word) (PDF)

Workbook References: NuLake IAS 2.5 pg 43, 44, 45

### Revision

Revision should include justification - for instance why is a network traversable. For Merit/Excellence, it should also include ideas about what would happen if an arc was added or deleted or weights changed etc.