PyTorch Geometric (PyG)

Overview

PyTorch Geometric is a library built on PyTorch for developing and training Graph Neural Networks (GNNs). Apply this skill for deep learning on graphs and irregular structures, including mini-batch processing, multi-GPU training, and geometric deep learning applications.

When to Use This Skill

This skill should be used when working with:

• Graph-based machine learning: Node classification, graph classification, link prediction
• Molecular property prediction: Drug discovery, chemical property prediction
• Social network analysis: Community detection, influence prediction
• Citation networks: Paper classification, recommendation systems
• 3D geometric data: Point clouds, meshes, molecular structures
• Heterogeneous graphs: Multi-type nodes and edges (e.g., knowledge graphs)
• Large-scale graph learning: Neighbor sampling, distributed training

Quick Start

Installation

uv pip install torch_geometric

For additional dependencies (sparse operations, clustering):

uv pip install pyg_lib torch_scatter torch_sparse torch_cluster torch_spline_conv -f https://data.pyg.org/whl/torch-${TORCH}+${CUDA}.html

Basic Graph Creation

import torch
from torch_geometric.data import Data

# Create a simple graph with 3 nodes
edge_index = torch.tensor([[0, 1, 1, 2],  # source nodes
                           [1, 0, 2, 1]], dtype=torch.long)  # target nodes
x = torch.tensor([[-1], [0], [1]], dtype=torch.float)  # node features

data = Data(x=x, edge_index=edge_index)
print(f"Nodes: {data.num_nodes}, Edges: {data.num_edges}")

Loading a Benchmark Dataset

from torch_geometric.datasets import Planetoid

# Load Cora citation network
dataset = Planetoid(root='/tmp/Cora', name='Cora')
data = dataset[0]  # Get the first (and only) graph

print(f"Dataset: {dataset}")
print(f"Nodes: {data.num_nodes}, Edges: {data.num_edges}")
print(f"Features: {data.num_node_features}, Classes: {dataset.num_classes}")

Core Concepts

Data Structure

PyG represents graphs using the torch_geometric.data.Data class with these key attributes:

• data.x: Node feature matrix [num_nodes, num_node_features]
• data.edge_index: Graph connectivity in COO format [2, num_edges]
• data.edge_attr: Edge feature matrix [num_edges, num_edge_features] (optional)
• data.y: Target labels for nodes or graphs
• data.pos: Node spatial positions [num_nodes, num_dimensions] (optional)
• Custom attributes: Can add any attribute (e.g., data.train_mask, data.batch)

Important: These attributes are not mandatory—extend Data objects with custom attributes as needed.

Edge Index Format

Edges are stored in COO (coordinate) format as a [2, num_edges] tensor:

• First row: source node indices
• Second row: target node indices

# Edge list: (0→1), (1→0), (1→2), (2→1)
edge_index = torch.tensor([[0, 1, 1, 2],
                           [1, 0, 2, 1]], dtype=torch.long)

Mini-Batch Processing

PyG handles batching by creating block-diagonal adjacency matrices, concatenating multiple graphs into one large disconnected graph:

• Adjacency matrices are stacked diagonally
• Node features are concatenated along the node dimension
• A batch vector maps each node to its source graph
• No padding needed—computationally efficient

from torch_geometric.loader import DataLoader

loader = DataLoader(dataset, batch_size=32, shuffle=True)
for batch in loader:
    print(f"Batch size: {batch.num_graphs}")
    print(f"Total nodes: {batch.num_nodes}")
    # batch.batch maps nodes to graphs

Building Graph Neural Networks

Message Passing Paradigm

GNNs in PyG follow a neighborhood aggregation scheme:

1. Transform node features
2. Propagate messages along edges
3. Aggregate messages from neighbors
4. Update node representations

Using Pre-Built Layers

PyG provides 40+ convolutional layers. Common ones include:

GCNConv (Graph Convolutional Network):

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

class GCN(torch.nn.Module):
    def __init__(self, num_features, num_classes):
        super().__init__()
        self.conv1 = GCNConv(num_features, 16)
        self.conv2 = GCNConv(16, num_classes)

    def forward(self, data):
        x, edge_index = data.x, data.edge_index
        x = self.conv1(x, edge_index)
        x = F.relu(x)
        x = F.dropout(x, training=self.training)
        x = self.conv2(x, edge_index)
        return F.log_softmax(x, dim=1)

GATConv (Graph Attention Network):

from torch_geometric.nn import GATConv

class GAT(torch.nn.Module):
    def __init__(self, num_features, num_classes):
        super().__init__()
        self.conv1 = GATConv(num_features, 8, heads=8, dropout=0.6)
        self.conv2 = GATConv(8 * 8, num_classes, heads=1, concat=False, dropout=0.6)

    def forward(self, data):
        x, edge_index = data.x, data.edge_index
        x = F.dropout(x, p=0.6, training=self.training)
        x = F.elu(self.conv1(x, edge_index))
        x = F.dropout(x, p=0.6, training=self.training)
        x = self.conv2(x, edge_index)
        return F.log_softmax(x, dim=1)

GraphSAGE:

from torch_geometric.nn import SAGEConv

class GraphSAGE(torch.nn.Module):
    def __init__(self, num_features, num_classes):
        super().__init__()
        self.conv1 = SAGEConv(num_features, 64)
        self.conv2 = SAGEConv(64, num_classes)

    def forward(self, data):
        x, edge_index = data.x, data.edge_index
        x = self.conv1(x, edge_index)
        x = F.relu(x)
        x = F.dropout(x, training=self.training)
        x = self.conv2(x, edge_index)
        return F.log_softmax(x, dim=1)

Custom Message Passing Layers

For custom layers, inherit from MessagePassing:

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

class CustomConv(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):
        # Add self-loops to adjacency matrix
        edge_index, _ = add_self_loops(edge_index, num_nodes=x.size(0))

        # Transform node features
        x = self.lin(x)

        # Compute normalization
        row, col = edge_index
        deg = degree(col, x.size(0), dtype=x.dtype)
        deg_inv_sqrt = deg.pow(-0.5)
        norm = deg_inv_sqrt[row] * deg_inv_sqrt[col]

        # Propagate messages
        return self.propagate(edge_index, x=x, norm=norm)

    def message(self, x_j, norm):
        # x_j: features of source nodes
        return norm.view(-1, 1) * x_j

Key methods:

• forward(): Main entry point
• message(): Constructs messages from source to target nodes
• aggregate(): Aggregates messages (usually don't override—set aggr parameter)
• update(): Updates node embeddings after aggregation

Variable naming convention: Appending _i or _j to tensor names automatically maps them to target or source nodes.

Working with Datasets

Loading Built-in Datasets

PyG provides extensive benchmark datasets:

# Citation networks (node classification)
from torch_geometric.datasets import Planetoid
dataset = Planetoid(root='/tmp/Cora', name='Cora')  # or 'CiteSeer', 'PubMed'

# Graph classification
from torch_geometric.datasets import TUDataset
dataset = TUDataset(root='/tmp/ENZYMES', name='ENZYMES')

# Molecular datasets
from torch_geometric.datasets import QM9
dataset = QM9(root='/tmp/QM9')

# Large-scale datasets
from torch_geometric.datasets import Reddit
dataset = Reddit(root='/tmp/Reddit')

Check references/datasets_reference.md for a comprehensive list.

Creating Custom Datasets

For datasets that fit in memory, inherit