Hi all,

Today, we're diving deep into the Graph Neural Networks, with appropriate mathematical intuition. What you all need is a basic understanding of how machine learning works and every maths that pre requisites it. Generally, its an advanced topic but the original 2009 paper version is not that hard. Without a further due, let's start!

In this article, we will cover the following topics:

1. Graph Representation
2. The Transition Function
3. State Convergence, Fixed Points & Contraction Mapping
4. The Output Function
5. Complete GNN Architecture
6. Training the GNN

1. Graph Representation

Ref : https://huggingface.co/blog/intro-graphml

Before we dive into neural networks, we need to understand how to represent graph datasets in a way machine can understand.

What is a Graph?

A graph G = (V, E) consists of:

• V: A set of nodes (vertices)
• E: A set of edges connecting these nodes

In the real world, graphs are everywhere:

• Social networks (people are nodes, friendships are edges)
• Molecules (atoms are nodes, bonds are edges) [My favorite part]