Graphs

What is a graph

A graph is an abstract data structure. It can be used to solve routine problems.

Vertices connected by an edge (see picture) are called Neighbours.

The degree of a vertex is how many things are connected to it, in the picture, there would be 2.

Edges can also be called connectors and vertex can also be called nodes or entries.

Terms

weighted graph

Each edge/arc has an associated value, which can be used for distance, cost and so on.

vertex/node

An entity, location within the graph (represented by a circle).

edge/arc

A connection between two vertex/nodes

undirected graph

You can travel either direction on an edge/arc. For example an edge between A & B allows movement from A to B and from B to A.

directed graph

Each edge/arc will have an arrow to indicate the direction of travel. This will require additional edges to cover both directions.

Adjacency Matrix

An adjacency matrix is a list showing the what vertexes are connected to their neighbors. This is represented by a list showing what vertex is connected to the other.

Adjacency List

This is a list shown in binary for the values that are going to be connected. It usually helps to transfer the matrices into a list first before you turn it into a graph to make things easier.

Comparison of List VS Matrix

Matrix	List
Its quicker to find an edge	Needs to look at all items
Less space, no wastage	Stores information about each edge