torch-geometric

PyTorch Geometric (PyG)

PyG is the standard library for Graph Neural Networks built on PyTorch. It provides data structures for graphs, 60+ GNN layer implementations, scalable mini-batch training, and support for heterogeneous graphs.

Install: uv add torch_geometric (or uv pip install torch_geometric; requires PyTorch). Optional: pyg-lib, torch-scatter, torch-sparse, torch-cluster for accelerated ops.

Core Concepts

Graph Data: Data and HeteroData

A graph lives in a Data object. The key attributes:

from torch_geometric.data import Data

data = Data(
    x=node_features,          # [num_nodes, num_node_features]
    edge_index=edge_index,     # [2, num_edges] — COO format, dtype=torch.long
    edge_attr=edge_features,   # [num_edges, num_edge_features]
    y=labels,                  # node-level [num_nodes, *] or graph-level [1, *]
    pos=positions,             # [num_nodes, num_dimensions] (for point clouds/spatial)
)

edge_index format is critical: it's a [2, num_edges] tensor where edge_index[0] = source nodes, edge_index[1] = target nodes. It is NOT a list of tuples. If you have edge pairs as rows, transpose and call .contiguous():

# If edges are [[src1, dst1], [src2, dst2], ...] — transpose first:
edge_index = edge_pairs.t().contiguous()

For undirected graphs, include both directions: edge (0,1) needs both [0,1] and [1,0] in edge_index.

For heterogeneous graphs, use HeteroData — see the Heterogeneous Graphs section below.

Datasets

PyG bundles many standard datasets that auto-download and preprocess:

from torch_geometric.datasets import Planetoid, TUDataset

# Single-graph node classification (Cora, Citeseer, Pubmed)
dataset = Planetoid(root='./data', name='Cora')
data = dataset[0]  # single graph with train/val/test masks

# Multi-graph classification (ENZYMES, MUTAG, IMDB-BINARY, etc.)
dataset = TUDataset(root='./data', name='ENZYMES')
# dataset[0], dataset[1], ... are individual graphs

Common datasets by task:

• Node classification: Planetoid (Cora/Citeseer/Pubmed), OGB (ogbn-arxiv, ogbn-products, ogbn-mag)
• Graph classification: TUDataset (MUTAG, ENZYMES, PROTEINS, IMDB-BINARY), OGB (ogbg-molhiv)
• Link prediction: OGB (ogbl-collab, ogbl-citation2)
• Molecular: QM7, QM9, MoleculeNet
• Point cloud/mesh: ShapeNet, ModelNet10/40, FAUST

Transforms

Transforms preprocess or augment graph data, analogous to torchvision transforms:

import torch_geometric.transforms as T

# Common transforms
T.NormalizeFeatures()    # Row-normalize node features to sum to 1
T.ToUndirected()         # Add reverse edges to make graph undirected
T.AddSelfLoops()         # Add self-loop edges
T.KNNGraph(k=6)          # Build k-NN graph from point cloud positions
T.RandomJitter(0.01)     # Random noise augmentation on positions
T.Compose([...])         # Chain multiple transforms

# Apply as pre_transform (once, saved to disk) or transform (every access)
dataset = ShapeNet(root='./data', pre_transform=T.KNNGraph(k=6),
                   transform=T.RandomJitter(0.01))

Building GNN Models

Quick Start: Using Built-in Layers

The fastest way to build a GNN — stack conv layers from torch_geometric.nn:

import torch
import torch.nn.functional as F
from torch_geometric.nn import GCNConv

class GCN(torch.nn.Module):
    def __init__(self, in_channels, hidden_channels, out_channels):
        super().__init__()
        self.conv1 = GCNConv(in_channels, hidden_channels)
        self.conv2 = GCNConv(hidden_channels, out_channels)

    def forward(self, x, edge_index):
        x = self.conv1(x, edge_index).relu()
        x = F.dropout(x, p=0.5, training=self.training)
        x = self.conv2(x, edge_index)
        return x

Important: PyG conv layers do NOT include activation functions — apply them yourself after each layer. This is by design for flexibility.

Choosing a Conv Layer

Pick based on your task and graph structure:

| Layer | Best for | Key idea | |-------|----------|----------| | GCNConv | Homogeneous, semi-supervised node classification | Spectral-inspired, degree-normalized aggregation | | GATConv / GATv2Conv | When neighbor importance varies | Attention-weighted messages | | SAGEConv | Large graphs, inductive settings | Sampling-friendly, learnable aggregation | | GINConv | Graph classification, maximizing expressiveness | As powerful as WL test | | TransformerConv | Rich edge features, complex interactions | Multi-head attention with edge features | | EdgeConv | Point clouds, dynamic graphs | MLP on edge features (x_i, x_j - x_i) | | RGCNConv | Heterogeneous with many relation types | Relation-specific weight matrices | | HGTConv | Heterogeneous graphs | Type-specific attention |

All conv layers accept (x, edge_index) at minimum. Many also accept edge_attr for edge features.

Lazy Initialization

Use -1 for input channels to let PyG infer dimensions automatically — especially useful for heterogeneous models:

conv = SAGEConv((-1, -1), 64)  # Input dims inferred on first forward pass
# Initialize lazy modules:
with torch.no_grad():
    out = model(data.x, data.edge_index)

High-Level Model APIs

For common architectures, PyG provides ready-made model classes:

from torch_geometric.nn import GraphSAGE, GCN, GAT, GIN

model = GraphSAGE(
    in_channels=dataset.num_features,
    hidden_channels=64,
    out_channels=dataset.num_classes,
    num_layers=2,
)

Custom Layers via MessagePassing

To implement a novel GNN layer, subclass MessagePassing. The framework is:

1. propagate() orchestrates the message passing
2. message() defines what info flows along each edge (the phi function)
3. aggregate() combines messages at each node (sum/mean/max)
4. update() transforms the aggregated result (the gamma function)

from torch_geometric.nn import MessagePassing
from torch_geometric.utils import add_self_loops, degree

class MyConv(MessagePassing):
    def __init__(self, in_channels, out_channels):
        super().__init__(aggr='add')  # "add", "mean", or "max"
        self.lin = torch.nn.Linear(in_channels, out_channels)

    def forward(self, x, edge_index):
        # Pre-processing before message passing
        x = self.lin(x)
        # Start message passing
        return self.propagate(edge_index, x=x)

    def message(self, x_j):
        # x_j: features of source nodes for each edge [num_edges, features]
        # The _j suffix auto-indexes source nodes, _i indexes target nodes
        return x_j

The _i / _j convention: any tensor passed to propagate() can be auto-indexed by appending _i (target/central node) or _j (source/neighbor node) in the message() signature. So if you pass x=... to propagate, you can access x_i and x_j in message().

Read references/message_passing.md for the full GCN and EdgeConv implementation examples.

Task-Specific Patterns

Node Classification

# Full-batch training on a single graph (e.g., Cora)
model.train()
for epoch in range(200):
    optimizer.zero_grad()
    out = model(data.x, data.edge_index)
    loss = F.cross_entropy(out[data.train_mask], data.y[data.train_mask])
    loss.backward()
    optimizer.step()

# Evaluation
model.eval()
pred = model(data.x, data.edge_index).argmax(dim=1)
acc = (pred[data.test_mask] == data.y[data.test_mask]).float().mean()

Graph Classification

Multiple graphs — use DataLoader for mini-batching and global pooling to get graph-level representations:

from torch_geometric.loader import DataLoader
from torch_geometric.nn import GCNConv, global_mean_pool

loader = DataLoader(dataset, batch_size=32, shuffle=True)

class GraphClassifier(torch.nn.Module):
    def __init__(self, in_ch, hidden_ch, out_ch):
        super().__init__()
        self.conv1 = GCNConv(in_ch, hidden_ch)
        self