Graph Machine Learning: Link Prediction on Social Networks

Hands on notebook from the Graph Machine Learning short course taught at the Semana da Computação 2025 (Computing Week) at the Federal University of Rondônia (UNIR).

Overview

Given a social network, can we guess which people are likely to become friends? This is the link prediction problem, one of the classic tasks in graph machine learning.

The notebook walks through a complete pipeline on real Facebook friendship data:

1. Load the friendship lists and build a graph with NetworkX
2. Create a balanced dataset of existing links (positives) and missing links (negatives)
3. Learn a vector representation for every user with Node2Vec
4. Turn each pair of users into a feature vector by combining their embeddings
5. Train a Random Forest to tell real links from fake ones
6. Evaluate the model with ROC AUC and explore its predictions interactively

What you will learn

• How to represent a social network as a graph and inspect it (nodes, edges, degrees)
• Why link prediction is framed as binary classification over node pairs
• How negative sampling creates the "no link" examples the model needs
• How Node2Vec uses biased random walks and Word2Vec to embed nodes in a vector space
• How the Hadamard product (element wise multiplication) turns two node embeddings into one edge feature
• How to evaluate a link predictor with ROC AUC and read its predicted probabilities
• How to visualize embeddings with PCA and explore predictions with interactive widgets

Pipeline

facebook/*.edges → NetworkX graph → positive + negative pairs → train / test split (80 / 20)
NetworkX graph → Node2Vec (32 dims) → Hadamard edge features → Random Forest → ROC AUC

Step	What happens	Key settings
Graph	Edge lists are merged into an undirected graph	nx.from_pandas_edgelist
Sampling	One negative pair is drawn for every existing edge	nx.non_edges, shuffled
Split	Pairs are split into train and test sets	test_size=0.2, random_state=42
Embeddings	Random walks are fed to a Word2Vec model	dimensions=32, walk_length=5, num_walks=10, window=3
Features	Embeddings of both endpoints are multiplied	wv[u] * wv[v]
Classifier	Random Forest on the edge features	n_estimators=100
Metric	Area under the ROC curve on the test set	roc_auc_score

Results

The model reaches a test ROC AUC of about 0.99 in the recorded run. The notebook also prints the predicted probability for 30 test pairs next to the expected answer, so participants can see where the model gets it right and where it fails.

The last cell opens an interactive explorer: pick a user from a dropdown, set a probability threshold and the number of suggestions, and the notebook draws that user's real friends (blue) together with the top predicted new friends (green, dashed edges). It works like a small "people you may know" feature.

Dataset

The facebook/ folder contains the ego-Facebook dataset from the Stanford Network Analysis Project (SNAP). It is made of 10 ego networks, each one centered on a survey participant, with anonymized user IDs.

Extension	Content
.edges	Friendships between the ego's friends, one pair of IDs per line
.circles	Friend circles (lists) defined by the ego
.feat / .egofeat	Anonymized binary profile features of each friend and of the ego
.featnames	Names of the feature dimensions

The notebook uses the graph structure only (the .edges files). Profile features and circles are left for experimentation.

Running the notebook

Google Colab (recommended)

This is how the course was run.

1. Click the Open in Colab badge above
2. Upload the facebook folder to /content/ in the Colab file panel, so the files end up at /content/facebook/
3. Run the cells from top to bottom

On a standard Colab machine, the Node2Vec step takes around 2 minutes and training the Random Forest takes around 10 minutes (the timings are noted in the notebook). The interactive explorer takes about a minute per user.

Locally

git clone https://github.com/Wyllgner/Graph_Machine_Learning_SDC25.git
cd Graph_Machine_Learning_SDC25
pip install node2vec networkx pandas numpy scikit-learn matplotlib ipywidgets tqdm jupyter
jupyter notebook

Before running, make two small changes to the notebook:

• In step 1, point folder_path to the local folder: folder_path = "facebook"
• In the imports cell, remove matplotlib.use('Agg') so the plots show up inside Jupyter

Notes for readers

The notebook is kept exactly as it was presented in the course. Anyone reusing it should know about two details:

• Duplicated node IDs. The loader also reads the .circles files. Those rows are dropped as empty, but along the way pandas turns the target column into floats, so the same user appears as "650" and as "650.0". This is why the graph shows 7,918 nodes and 168,486 edges, exactly twice the real 3,959 nodes and 84,243 edges of the .edges files. Reading only files ending in .edges and loading IDs as strings (dtype=str) fixes it.
• Optimistic score. Node2Vec is trained on the full graph, including the links that are later used as test positives, so the test AUC is higher than it would be on truly unseen links. A stricter setup removes the test edges from the graph before computing the embeddings.

Both points make good follow up exercises after going through the course.

Repository structure

Path	Description
Curso_GML_2025 (1).ipynb	Course notebook (comments and outputs in Portuguese)
facebook/	SNAP ego-Facebook dataset
README.md	This file

Credits

• Course taught by Wyllgner França at the Semana da Computação 2025, UNIR
• Dataset: J. McAuley and J. Leskovec. Learning to Discover Social Circles in Ego Networks. NIPS, 2012
• Node2Vec: A. Grover and J. Leskovec. node2vec: Scalable Feature Learning for Networks. KDD, 2016