Graph Tasks: Node, Edge, and Graph-Level Prediction

Why Task Level Matters

The task level determines:

• What labels you have (per node, per edge, per graph)
• What output head you attach after the GNN
• How you compute the loss
• Whether you need graph pooling

The GNN backbone — the stack of message-passing layers that produces node embeddings — is broadly the same. The key differences are in what you do with those embeddings at the end.

Task 1: Node-Level Prediction

What: predict a property for each node.

Examples:

• Citation networks: classify each paper’s topic (Cora, CiteSeer, ogbn-arxiv)
• Social networks: predict user engagement or spam likelihood
• Protein interaction networks: predict protein function
• Traffic networks: predict traffic speed at each sensor node

Output head:

h_v ∈ ℝ^d  →  Linear(h_v)  →  ŷ_v ∈ ℝ^C

Apply a linear (or MLP) classifier to each node embedding independently.

Training setup: many node-level tasks use a single large graph with a split into labelled train/validation/test nodes. The GNN processes the full graph (including test nodes) but is supervised only on train nodes — this is transductive learning. New nodes at test time can see other test nodes’ features through message passing.

Inductive setting: you may also train on one set of graphs and test on entirely new graphs (e.g., PPI dataset). Then test nodes cannot attend to train nodes.

Task 2: Edge-Level Prediction

What: predict a property for a pair of nodes (u, v) — whether an edge should exist, or what type it is.

Examples:

• Recommender systems: will user u click on item v?
• Knowledge graph completion: does the relation (head, relation, tail) hold?
• Drug-target interaction: does drug u bind protein v?
• Friendship prediction in social networks

Output head:

h_u, h_v ∈ ℝ^d  →  f(h_u, h_v)  →  ŷ_{uv} ∈ ℝ

Where f is a scoring function (dot product, concatenation + MLP, Hadamard product + MLP).

Training setup: typically, the training edges are used to compute node embeddings, and a subset of edges (plus negative samples) are used as supervision. Care must be taken not to include test edges in the message-passing graph during training.

Negative sampling: since most pairs of nodes are not connected, you must sample negative edges (non-existing pairs) for training. The ratio of positives to negatives is a key hyperparameter.

Task 3: Graph-Level Prediction

What: predict a property of the entire graph.

Examples:

• Drug discovery: predict if a molecule is toxic or active against a target (QM9, ZINC, OGB-molhiv)
• Chemical property prediction: HOMO-LUMO gap, solubility
• Graph classification: classify graph types (social network vs citation vs random)
• Counting substructures: does the graph contain a specific motif?

Output head:

{h_v : v ∈ V}  →  READOUT  →  h_G ∈ ℝ^d  →  Linear  →  ŷ_G

The READOUT (also called pooling or global pooling) aggregates all node embeddings into a single graph embedding. Common choices:

• Global mean pool: h_G = mean({h_v})
• Global sum pool: h_G = sum({h_v})
• Global max pool: h_G = max({h_v})
• Hierarchical pooling: DiffPool, TopKPool

Training setup: each graph is an independent data point. Standard train/val/test split across graphs. Multiple graphs per batch (mini-batch training with graph-level batching).

Task 4: Node Regression

Like node classification but predicting a continuous value per node.

Examples:

• Traffic speed prediction at sensor nodes
• Energy of atoms in a molecule
• Epidemic spreading level at city nodes

Output head: same as node classification but with MSE loss instead of cross-entropy.

Task 5: Graph Regression

Predict a continuous value for the whole graph.

Examples:

• Molecular property prediction (energy, HOMO-LUMO gap) — QM9 benchmark
• Graph-level count prediction

Summary

All tasks share the same GNN backbone. Mastering graph-level tasks requires understanding pooling (next: the Pooling section). Understanding node-level tasks requires understanding message passing (GCN, GAT, GIN posts). Edge tasks bridge both.

References

• Hamilton, W. L., Ying, R., & Leskovec, J. (2017). Inductive Representation Learning on Large Graphs. NeurIPS 2017 (GraphSAGE — introduces the node/link/graph task taxonomy).
• Bronstein, M. M., Bruna, J., Cohen, T., & Veličković, P. (2021). Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges. arXiv preprint.