General Maths Unit 2 – NETWORKS

BASIC CONCEPTS OF NETWORKSNetwork

A Network is a graphical representation of objects

connected in various ways i.e. a Family Tree

Vertex/Vertices(Node)Are the objects in a network.

i.e. A, B, C and D are all Vertices

Edge(Path)

The lines connecting each Vertex 1, 2, 3, 4, and 5 are

called Edges or PathsUndirected Network(Graph)Is a network where no arrows

exist on the Edges

i.e. The A computer is connected to the B, D and C computers, but not directly to

the E computer.

Directed Network(Graph)Is a network where arrows

exist on the Edges to indicate the direction of the flow.

i.e. As in one way streets, you can travel from B to C but not

C to B.

Degree of a Vertex(Node)The Degree of a Vertex is the number of the Edges going

into the Vertex.

i.e. Vertex U has a Degree of 3.

Parallel/Multiple EdgesWhere a vertex has multiple

connections to another vertex.

i.e. Town C to D has a Multiple Edge (note: Town C degree=4)

LoopsIs where a vertex has an Edge

connected to itself.

i.e. Vertex D has a Loop (note: The degree of Vertex D is 5)

Simple GraphA Simple Graph has no Loops

or Multiple Edges

i.e. This is an example of a Simple Graph

PathA Path connects Vertices in a

Network.

i.e. A possible Path from Vertex A to E is A-B-C-E

CircuitA Circuit is a Path which starts and ends at the same Vertex.

i.e. A possible Circuit for Vertex C is C-D-C

Unconnected Networks and Isolated Vertices

When a Path does not exist between all Vertices it is called

an Unconnected Network.

i.e. Vertex 3 is also IsolatedRegions

Regions are the amount of enclosed Spaces in the Graph plus 1 for the outside Region.

i.e. This network has 7 Regions

Sub GraphsA Sub Graph is a section of a

Graph

i.e. The Network on the right is a Sub Graph of the left network

Planar NetworksA Planar Network must have

No Crossing Edges

i.e. Not Planar because Edge A-C and A-E cross Edge B-D