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Introduction to Graphs in Python

Last Updated : 23 Jul, 2025

Graph is a non-linear data structure consisting of vertices and edges. The vertices are sometimes also referred to as nodes and the edges are lines or arcs that connect any two nodes in the graph. More formally a Graph is composed of a set of vertices( V ) and a set of edges( E ). The graph is denoted by G(V, E).

Imagine a game of football as a web of connections, where players are the nodes and their interactions on the field are the edges. This web of connections is exactly what a graph data structure represents, and it’s the key to unlocking insights into team performance and player dynamics in sports.

👁 Introduction-to-Graphs
Introduction to Graphs

Components of Graph Data Structure

  • Vertices: Vertices are the fundamental units of the graph. Sometimes, vertices are also known as vertex or nodes. Every node/vertex can be labeled or unlabelled.
  • Edges: Edges are drawn or used to connect two nodes of the graph. It can be ordered pair of nodes in a directed graph. Edges can connect any two nodes in any possible way. There are no rules. Sometimes, edges are also known as arcs. Every edge can be labelled/unlabelled.

explore in detail about - Types of Graphs in Data Structures and Algorithms

Representation of Graph Data Structure

There are multiple ways to store a graph, following are the most common representations:

  • Adjacency Matrix Representation
  • Adjacency List Representation

Adjacency Matrix Representation of Graph Data Structure

In this method, the graph is stored in the form of the 2D matrix where rows and columns denote vertices. Each entry in the matrix represents the weight of the edge between those vertices. 

👁 adjacency_mat1-(1)-copy

Below is the Python implementation of Graph Data Structure represented using Adjacency Matrix:


Output
Adjacency Matrix:
0 1 1 0
1 0 1 0
1 1 0 1
0 0 1 0

Explore in detail about - Adjacency Matrix Representation

Adjacency List Representation of Graph

This graph is represented as a collection of linked lists. There is an array of pointer which points to the edges connected to that vertex. 

👁 adjacency_list

Below is the Python implementation of Graph Data Structure represented using Adjacency List:


Output
Adjacency List Representation:
0: 1 2 
1: 0 2 
2: 0 1 3 
3: 2

Explore in detail about - Adjacency List Representation

Comparison between Adjacency Matrix and Adjacency List

When the graph contains a large number of edges then it is good to store it as a matrix because only some entries in the matrix will be empty. An algorithm such as Prim’s and Dijkstra adjacency matrix is used to have less complexity.

ActionAdjacency MatrixAdjacency List
Adding EdgeO(1)O(1)
Removing an edgeO(1)O(N)
InitializingO(N*N)O(N)

Basic Operations on Graph Data Structure

Below are the basic operations on the graph:

Difference between Tree and Graph

Tree is a restricted type of Graph Data Structure, just with some more rules. Every tree will always be a graph but not all graphs will be trees. Linked List, Trees, and Heaps all are special cases of graphs. 

👁 tree_vs_graph
Tree vs Graph

read more about - Real-Life Applications, Advantages and Disadvantages of Graph Data Structure

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