12-Step Hand-Calculated Guide to Graph Neural Networks
ProfTomYeh · x · 2026-07-15
Using hand-drawn matrices and manual calculations, the author breaks down the underlying mechanics of Graph Neural Networks (GCN), completing a node classification task on a small 5-node graph.
Core Calculation Steps:
- Adjacency Matrix: Constructing a matrix that includes self-loops (the node itself) and neighbor connections.
- Message Passing & Pooling: Node features are transformed via weight and bias matrices, activated by ReLU, and then aggregated with neighbor information using the adjacency matrix.
- Classification Output: After passing through two GCN layers and a fully connected layer, a Sigmoid function compresses the scores into probabilities to classify all nodes.
Key Insight: GCN layers and Transformer layers share a highly similar structure. GCNs use a fixed adjacency matrix to mix information between nodes, whereas Transformers use a dynamically computed attention matrix (based on Q, K, V) to mix information between tokens.
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