Graph Neural Networks

Graph Neural Networks: Teaching Machines to Understand Connections

The Story of the Social Butterfly

Imagine you’re at a big party. There are lots of people talking to each other. Some people know many others, some know just a few. Now, what if you wanted to find out who the most popular person is? Or which groups of friends hang out together?

You’d look at the CONNECTIONS between people, not just the people themselves!

This is exactly what Graph Neural Networks (GNNs) do. They help machines understand things that are connected—like friends, roads between cities, or atoms in a molecule.

What We’ll Learn Together

graph TD
    A["Graph Data Structures"] --> B["Graph Convolutional Networks"]
    B --> C["Graph Attention Networks"]
    C --> D["Node & Graph Classification"]
    style A fill:#FF6B6B,color:white
    style B fill:#4ECDC4,color:white
    style C fill:#45B7D1,color:white
    style D fill:#96CEB4,color:white

Part 1: Graph Data Structures

What is a Graph?

Think of a graph like a friendship map.

• Nodes (Vertices): These are the dots—each dot is a person, a city, or anything you want to represent
• Edges: These are the lines connecting dots—they show who is friends with whom, or which roads connect cities

A Simple Example

Imagine three kids: Ali, Ben, and Cat.

• Ali is friends with Ben
• Ben is friends with Cat
• Ali is NOT friends with Cat (yet!)

graph LR
    Ali((Ali)) --- Ben((Ben))
    Ben --- Cat((Cat))
    style Ali fill:#FF6B6B,color:white
    style Ben fill:#4ECDC4,color:white
    style Cat fill:#45B7D1,color:white

This is a graph! Ali, Ben, and Cat are nodes. The friendships are edges.

Why Graphs Matter

Regular data (like a list of numbers) is like people standing in a line—one after another.

But the REAL WORLD is messy and connected:

• Social networks (who follows whom)
• Molecules (atoms bonded together)
• Maps (cities connected by roads)
• The internet (websites linked together)

Graphs capture RELATIONSHIPS. And relationships matter!

Key Graph Concepts

Node Features

Each node can have information attached. Think of it like a profile card:

Node: Ali

• Age: 8
• Favorite color: Blue
• Has a pet: Yes

These details are called node features. GNNs use these features to learn!

Directed vs Undirected Graphs

Undirected: Like friendship—if Ali is Ben’s friend, Ben is Ali’s friend too.

Directed: Like following on social media—Ali follows Ben, but Ben might not follow Ali back.

graph LR
    subgraph Undirected
    A1((A)) --- B1((B))
    end
    subgraph Directed
    A2((A)) --> B2((B))
    end

Part 2: Graph Convolutional Networks (GCNs)

The Neighborhood Averaging Trick

Here’s a magical idea: You become more like your friends over time.

If all your friends love pizza, you might start loving pizza too! GCNs work the same way.

A node learns by looking at its neighbors.

How GCNs Work

Imagine you want to guess what color Ali likes. You don’t just look at Ali—you also look at Ali’s friends!

Step-by-Step:

1. Gather: Collect information from all neighbors
2. Average: Mix all that information together
3. Update: Use this to update Ali’s own information
4. Repeat: Do this multiple times!

graph TD
    A["Ali wants to learn"] --> B["Look at neighbors"]
    B --> C["Collect their info"]
    C --> D["Mix it together"]
    D --> E[Update Ali's info]
    E --> F["Ali knows more now!"]
    style A fill:#FF6B6B,color:white
    style F fill:#4ECDC4,color:white

The GCN Formula (Made Simple!)

Don’t worry—this looks scary but it’s just math for:

“Take info from neighbors, mix it, and learn”

New_Info(Ali) = Mix(Ali's info + Ben's info + ...)

Each time we do this mixing, Ali “knows” about nodes further away!

This is called “message passing”—nodes send messages to each other!

A Real Example: Predicting Movie Preferences

Imagine a graph where:

• Nodes = People
• Edges = They watched the same movie
• Features = Movies each person liked

GCN can predict: What movies will YOU like?

It looks at what your “movie neighbors” enjoyed and suggests similar films!

Part 3: Graph Attention Networks (GATs)

Not All Friends Are Equal

Here’s the truth: Some friends influence you more than others.

Your best friend’s opinion matters more than someone you barely know, right?

Graph Attention Networks understand this!

The Attention Mechanism

GAT adds a superpower: Paying more attention to important neighbors.

Think of it like this:

• GCN: Treats all friends equally (everyone gets one vote)
• GAT: Best friends get MORE votes!

graph TD
    A["Ali's neighbors] --> B{How important?}
    B -->|Very important| C[Big influence]
    B -->|Less important| D[Small influence]
    C --> E[Ali's final decision"]
    D --> E
    style C fill:#FF6B6B,color:white
    style D fill:#4ECDC4,color:white
    style E fill:#45B7D1,color:white

How Attention Works

1. Look at each neighbor
2. Ask: “How relevant is this neighbor to me?”
3. Give higher scores to more relevant neighbors
4. Use these scores when mixing information

Simple Example

Ali wants to decide what game to play:

• Best friend Ben says: “Let’s play soccer!” (Attention: 0.7)
• Acquaintance Dan says: “Let’s play chess!” (Attention: 0.3)

Ali listens to Ben more because Ben matters more!

Final decision = 70% soccer influence + 30% chess influence

Why Attention is Powerful

GATs are like having a smart filter that knows whose opinion to trust!

Multi-Head Attention

Sometimes, different aspects matter differently.

• For homework help, you might listen to the smart friend
• For fashion advice, you might listen to the stylish friend

Multi-head attention = Looking at things from MULTIPLE perspectives at once!

It’s like having several pairs of eyes, each looking for something different.

Part 4: Node and Graph Classification

Two Types of Questions

GNNs can answer two different kinds of questions:

1. Node Classification: What type is THIS specific node?
2. Graph Classification: What type is the WHOLE graph?

Node Classification

Question: What category does ONE node belong to?

Example: Social Network

In a social network:

• Some people are influencers (many followers)
• Some are regular users (few connections)
• Some are bots (weird patterns)

Node classification predicts the type of EACH person!

graph TD
    subgraph "Node Classification"
    A((User A)) --> |Type?| T1["Influencer"]
    B((User B)) --> |Type?| T2["Regular"]
    C((User C)) --> |Type?| T3["Bot"]
    end
    style T1 fill:#FF6B6B,color:white
    style T2 fill:#4ECDC4,color:white
    style T3 fill:#45B7D1,color:white

How Node Classification Works

1. Run GNN on the graph (each node learns from neighbors)
2. Each node now has “smart” features (after message passing)
3. Use a classifier to predict each node’s type
4. Train by comparing predictions to known labels

Real Applications

Graph Classification

Question: What category does the ENTIRE graph belong to?

Example: Molecule Classification

A molecule is a graph:

• Nodes = Atoms (carbon, oxygen, etc.)
• Edges = Bonds between atoms

Is this molecule a medicine or a poison?

We need to look at the WHOLE structure, not just one atom!

How Graph Classification Works

1. Run GNN on the entire graph
2. Combine all node features into ONE graph feature
3. This is called “Graph Pooling”
4. Classify the whole graph based on this combined feature

graph TD
    A["All nodes with features"] --> B["Combine/Pool"]
    B --> C["One vector for whole graph"]
    C --> D["Classify the graph"]
    style B fill:#FF6B6B,color:white
    style C fill:#4ECDC4,color:white
    style D fill:#45B7D1,color:white

Graph Pooling Methods

How do we combine all nodes into one representation?

Real-World Applications

Node Classification Examples

• Academic papers: What topic is this paper about?
• Proteins: What function does this protein have?
• Fraud detection: Is this transaction suspicious?

Graph Classification Examples

• Drug discovery: Will this molecule cure a disease?
• Social analysis: Is this network a community or random?
• Chemistry: Is this compound toxic?

The Big Picture

graph TD
    A["Data as Graphs"] --> B["GCN: Learn from neighbors"]
    B --> C["GAT: Pay attention to important neighbors"]
    C --> D{What to predict?}
    D -->|Single nodes| E["Node Classification"]
    D -->|Whole graphs| F["Graph Classification"]
    style A fill:#FF6B6B,color:white
    style B fill:#4ECDC4,color:white
    style C fill:#45B7D1,color:white
    style E fill:#96CEB4,color:white
    style F fill:#DDA0DD,color:white

Summary: What We Learned

You Did It!

Graph Neural Networks might sound complex, but the core idea is simple:

Things that are connected influence each other. GNNs learn these influences.

Next time you see a social network, a molecule, or a map—remember, there’s a GNN that could understand it!

Now go forth and see graphs everywhere!