Graph Theory for Machine Learning
Graphs are the data structure of relationships. If your data has connections, you need graph theory. Language: Python Build a graph class with adjacency matrix/list representations and implement BFS and DFS traversals. Compute the graph Laplacian and use its eigenvalues to detect connected components and cluster nodes. Implement one round of GNN-style message passing as a normalized adjacency matrix multiplication. Apply spectral clustering to partition a graph using the Fiedler vector. Social networks, molecules, knowledge bases, citation networks, road maps -- all are graphs. Traditional ML treats data as flat tables. Each row is independent. Each feature is a column. But when the structure of connections matters, tables fail. Consider a social network. You want to predict what product a user will buy. Their purchase history matters. But their friends' purchase history matters more. The connections carry signal. Or consider a molecule. You want to predict if it binds to a protein. The atoms matter, but what really matters is how atoms are bonded to each other. The structure is the data. Graph Neural Networks (GNNs) are the fastest-growing area in deep learning. They power drug discovery, social recommendation, fraud detection, and knowledge graph reasoning. Every GNN builds on the same foundation: basic graph theory. You need four things: A way to represent graphs as matrices (so you can multiply…
Graph Theory for Machine Learning: Graphs are the data structure of relationships. If your data has connections, you need graph theory.
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