Networks- More About

Mathematics is concerned with relationships between things. Network diagrams are a useful way to record and study these relationships.

Some networks have important and interesting mathematical properties, but the inclusion of networks in VELS is to develop students’ ability to represent and organise information. This is an important generic problem solving skill, which all students need to develop for adult life.

Examples of networks include road maps, electricity distribution network, family trees, the Nine men's Morris board game, organisational charts in companies, flowcharts of jobs to be done, electrical wiring diagrams, public transport maps, tree diagrams to illustrate combinations of outcomes, net of a solid.

The key feature of networks is that they always have ‘nodes’ and ‘lines’.

• The nodes (also called points or vertices) represent people, places, events, etc.
• The lines (also called edges or arcs) represent the presence of a specified relationship between the nodes.

The VELS glossary describes a network as follows: A set of points (vertices or nodes) some of which are joined by lines or curves (edges) which sometimes enclose regions (faces). Networks are used to represent relationships involving connectedness, for example road networks.

The key to creating a successful network, and to interpreting one, is to identify very clearly at the outset exactly what relationship is being represented by the lines. A network is a model of reality, and as such, it does not include all the features of the real situation.

Sometimes the lines are arrows to indicate a direction to the relationship. For example, the relationship ‘is the child of’ has a direction. I am my mother’s child. She cannot be my child. This makes a ‘directed network’.

Sometimes there is more than one relationship represented on a network. For example a family tree has one sort of connecting line to represent ‘is a child of’ and another sort to represent ‘is married to’. Usually, however, there is only one relationship represented.

Venn diagrams, two way tables and Karnaugh maps, and tables more generally are other devices for organising and recording information that students will encounter.