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:

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.conv2 = GCNConv(hidden_ch, hidden_ch)
        self.lin = torch.nn.Linear(hidden_ch, out_ch)

    def forward(self, x, edge_index, batch):
        x = self.conv1(x, edge_index).relu()
        x = self.conv2(x, edge_index).relu()
        x = global_mean_pool(x, batch)  # [num_graphs_in_batch, hidden_ch]
        return self.lin(x)

# Training loop
for data in loader:
    out = model(data.x, data.edge_index, data.batch)
    loss = F.cross_entropy(out, data.y)

PyG's DataLoader batches multiple graphs by creating block-diagonal adjacency matrices. The batch tensor maps each node to its graph index. Pooling ops (global_mean_pool, global_max_pool, global_add_pool) use this to aggregate per-graph.

Link Prediction

Split edges into train/val/test, use negative sampling:

from torch_geometric.transforms import RandomLinkSplit

transform = RandomLinkSplit(
    num_val=0.1,
    num_test=0.1,
    is_undirected=True,
    add_negative_train_samples=False,
)
train_data, val_data, test_data = transform(data)

# Encode nodes, then score edges
z = model.encode(train_data.x, train_data.edge_index)
# Positive edges
pos_score = (z[train_data.edge_label_index[0]] * z[train_data.edge_label_index[1]]).sum(dim=1)

Read references/link_prediction.md for the complete link prediction guide: GAE/VGAE autoencoders, full training loops, LinkNeighborLoader for large graphs, heterogeneous link prediction, and evaluation metrics.

Scaling to Large Graphs

For graphs that don't fit in GPU memory, use neighbor sampling via NeighborLoader:

from torch_geometric.loader import NeighborLoader

train_loader = NeighborLoader(
    data,
    num_neighbors=[15, 10],     # Sample 15 neighbors in hop 1, 10 in hop 2
    batch_size=128,              # Number of seed nodes per batch
    input_nodes=data.train_mask, # Which nodes to sample from
    shuffle=True,
)

for batch in train_loader:
    batch = batch.to(device)
    out = model(batch.x, batch.edge_index)
    # Only use first batch_size nodes for loss (these are the seed nodes)
    loss = F.cross_entropy(out[:batch.batch_size], batch.y[:batch.batch_size])

Key points about NeighborLoader:

• num_neighbors list length should match GNN depth (number of message passing layers)
• Seed nodes are always the first batch.batch_size nodes in the output
• batch.n_id maps relabeled indices back to original node IDs
• Works for both Data and HeteroData
• For link prediction, use LinkNeighborLoader instead
• Sampling more than 2-3 hops is generally infeasible (exponential blowup)

Other scalability options: ClusterLoader (ClusterGCN), GraphSAINTSampler, ShaDowKHopSampler. For multi-GPU training, DDP, PyTorch Lightning integration, and torch.compile support, read references/scaling.md.

Heterogeneous Graphs

For graphs with multiple node and edge types (social networks, knowledge graphs, recommendation):

from torch_geometric.data import HeteroData

data = HeteroData()

# Node features — indexed by node type string
data['user'].x = torch.randn(1000, 64)
data['movie'].x = torch.randn(500, 128)

# Edge indices — indexed by (src_type, edge_type, dst_type) triplet
data['user', 'rates', 'movie'].edge_index = torch.randint(0, 500, (2, 3000))
data['user', 'follows', 'user'].edge_index = torch.randint(0, 1000, (2, 5000))

# Access convenience dicts
data.x_dict        # {'user': tensor, 'movie': tensor}
data.edge_index_dict  # {('user','rates','movie'): tensor, ...}
data.metadata()    # ([node_types], [edge_types])

Three ways to build heterogeneous GNNs

1. Auto-convert with to_hetero() — write a homogeneous model, convert automatically:

from torch_geometric.nn import SAGEConv, to_hetero

class GNN(torch.nn.Module):
    def __init__(self, hidden_channels, out_channels):
        super().__init__()
        self.conv1 = SAGEConv((-1, -1), hidden_channels)
        self.conv2 = SAGEConv((-1, -1), out_channels)

    def forward(self, x, edge_index):
        x = self.conv1(x, edge_index).relu()
        x = self.conv2(x, edge_index)
        return x

model = GNN(64, dataset.num_classes)
model = to_hetero(model, data.metadata(), aggr='sum')

# Now accepts dicts:
out = model(data.x_dict, data.edge_index_dict)

Use (-1, -1) for bipartite input channels (source, target may differ). Lazy init handles the rest.

2. HeteroConv wrapper — different conv per edge type:

from torch_geometric.nn import HeteroConv, GCNConv, SAGEConv, GATConv

conv = HeteroConv({
    ('paper', 'cites', 'paper'): GCNConv(-1, 64),
    ('author', 'writes', 'paper'): SAGEConv((-1, -1), 64),
    ('paper', 'rev_writes', 'author'): GATConv((-1, -1), 64, add_self_loops=False),
}, aggr='sum')

3. Native heterogeneous operators like HGTConv:

from torch_geometric.nn import HGTConv
conv = HGTConv(hidden_channels, hidden_channels, data.metadata(), num_heads=4)

Important for heterogeneous graphs:

• Use T.ToUndirected() to add reverse edge types for bidirectional message flow
• Disable add_self_loops in bipartite conv layers (different source/dest types) — use skip connections instead: conv(x, edge_index) + lin(x)
• For NeighborLoader on HeteroData, specify input_nodes as ('node_type', mask) tuple
• num_neighbors can be a dict keyed by edge type for fine-grained control

Read references/heterogeneous.md for complete examples including training loops and NeighborLoader usage with heterogeneous graphs.

Custom Datasets

For loading your own data into PyG:

• Quick (no class needed): Create Data objects directly and pass a list to DataLoader
• Reusable (fits in RAM): Subclass InMemoryDataset — override raw_file_names, processed_file_names, download(), process()
• Large (disk-backed): Subclass Dataset — also override len() and get()
• From CSV: Load node/edge tables with pandas, build mappings to consecutive indices, assemble into Data or HeteroData
• From NetworkX: from_networkx(G) converts a NetworkX graph directly
• From scipy sparse: from_scipy_sparse_matrix(adj) extracts edge_index

Read references/custom_datasets.md for complete examples with all patterns, CSV loading with encoders, and the MovieLens walkthrough.

Explainability

PyG provides torch_geometric.explain for interpreting GNN predictions:

from torch_geometric.explain import Explainer, GNNExplainer

explainer = Explainer(
    model=model,
    algorithm=GNNExplainer(epochs=200),
    explanation_type='model',
    node_mask_type='attributes',
    edge_mask_type='object',
    model_config=dict(
        mode='multiclass_classification',
        task_level='node',
        return_type='log_probs',
    ),
)

explanation = explainer(data.x, data.edge_index, index=10)
explanation.visualize_graph()           # Important subgraph
explanation.visualize_feature_importance(top_k=10)  # Feature importance

Available algorithms: GNNExplainer (optimization-based), PGExplainer (parametric, trained), CaptumExplainer (gradient-based via Captum), AttentionExplainer (attention weights). Works for both homogeneous and heterogeneous graphs.

Read references/explainability.md for all algorithms, heterogeneous explanations, evaluation metrics, and PGExplainer training.

Common Pitfalls

1. edge_index shape: Must be [2, num_edges], not [num_edges, 2]. Transpose if needed.
2. Forgetting activations: Conv layers don't include ReLU/etc — add them manually.
3. Self-loops in hetero bipartite: Don't use add_self_loops=True when source and dest node types differ. Use skip connections instead.
4. NeighborLoader slicing: Only the first batch.batch_size nodes are your seed nodes. Slice predictions and labels accordingly.
5. Undirected graphs: If your graph is undirected, include edges in both directions in edge_index, or use T.ToUndirected().
6. Lazy init: Models with -1 input channels need one forward pass with torch.no_grad() before training to initialize parameters.
7. Global pooling for graph tasks: Use global_mean_pool(x, batch) (not manual reshape) to aggregate node features to graph-level.
8. num_neighbors alignment: Keep len(num_neighbors) equal to the number of GNN layers. More hops than layers wastes compute; fewer means wasted model capacity.