Graph Convolutional Networks computed by hand in 12 steps: GCN is the transformer's little cousin

ProfTomYeh · x · 2026-09-13

ProfTomYeh walks through a full two-layer GCN on a five-node graph, computing every matrix by hand:

Each GCN layer: adjacency + self-loops (A+I) → weights/biases + ReLU to build messages → adjacency-matrix pooling to aggregate neighbor messages, then a second layer, a fully-connected layer, a linear layer, and sigmoid for per-node classification (A: 0, B/C/D: 1, E: 0.5).
Key analogy: a GCN layer = pooling via adjacency matrix + an MLP per node; a transformer layer has the same two parts with attention replacing the fixed adjacency matrix — hence "the transformer's little cousin, just more stubborn because its attention is fixed by the graph."

More from Research