Implementing a Graph in Python

A graph is a data structure used to illustrate connections between two objects. A simple example of a graph is a geographical map in which different places are connected by roads. In this article, we will study the theoretical aspects of a graph data structure. Additionally, we will implement a graph using two different methods. 

What is a graph?

A graph is a non-linear data structure that is used to represent interconnected objects. The objects are termed vertices and the link between them are called edges.

Mathematically, A graph G is defined as an ordered pair of two sets V and E. It is represented as G=(V,E) where,

• V is the set of vertices or vertices present in the graph.
• E is the set of edges present in the graph. Each edge is represented using a tuple which shows the vertices it is connected to. For example, if an edge ‘e’ is connecting vertices v1 and v2, it will be represented as (v1,v2).

To understand this more clearly, let’s look at the following example.

In the above figure, we have a graph containing 6 vertices namely 0,1,2,3,4,5. Thus the set V in the equation of G=(V, E) will be the set of vertices which will be represented as follows.