GCN

Graph Convolutional Network — Kipf & Welling, ICLR 2017 (arXiv:1609.02907).

The reference baseline of the field, and in graphnetz's own findings still the model that takes the most categories.

What it computes

Each layer averages a node's neighbourhood under a symmetric degree normalisation, then applies a linear map:

\[H^{(l+1)} \;=\; \sigma\!\left(\tilde{D}^{-1/2}\,\tilde{A}\,\tilde{D}^{-1/2}\,H^{(l)}\,W^{(l)}\right)\]

with \(\tilde{A} = A + I\) the adjacency plus self-loops and \(\tilde{D}\) its degree matrix. The normalisation is the substantive choice: a neighbour of degree \(d_j\) contributes with weight \(1/\sqrt{d_i d_j}\), so a hub influences each of its many neighbours only weakly.

Architecture as shipped

Two GCNConv layers with a ReLU between them, no dropout:

GCN(in_channels, hidden_channels, out_channels)

layers	2
activation	ReLU
dropout	none
parameters	in × hidden + hidden × out, plus biases
supported tasks	all four, via adapters

Two layers means a two-hop receptive field. That is not a placeholder: GCN degrades with depth rather than improving, because repeated normalised averaging drives node representations toward a degree-dependent fixed point — oversmoothing. The original paper found two layers best on citation graphs and so does everyone since.

Where it does well, and why

GCN's normalisation encodes an assumption: a node resembles its neighbours, and a high-degree neighbour is less informative per edge. That holds on citation networks and on many infrastructure and routing graphs, and the findings bear it out — GCN wins Social (Cora), Knowledge (FB15k-237), Computing (Internet AS) and Physics (Ising lattice).

The same assumption is what hurts it on heterophilic graphs, where connected nodes tend to differ, and where the averaging washes out the contrast the label depends on. GraphSAGE, which keeps the self representation on its own weights, is the natural comparison there.

The strongest baseline is a real result

In the ten-category sweep GCN takes the most rows of any model while ranking second by mean rank, and the Friedman omnibus does not reject. A two-layer 2017 baseline being indistinguishable from three later architectures is the finding, not a failure to tune it. See Findings.

Usage

from graphnetz import GCN, run_benchmark, train_node_classification
from graphnetz.datasets.social import cora

# Directly
ds = cora("data/cora")
model = GCN(ds.num_features, 64, ds.num_classes)
history = train_node_classification(model, ds[0], epochs=200)

# In a benchmark
report = run_benchmark("social", {"GCN": GCN}, seeds=range(10), task_type="node_cls")

API

Full signature, parameters and source: graphnetz.models.GCN.