Unifying Graph Convolutional Neural Networks and Label Propagation

Hongwei Wang, J. Leskovec

Main figure for Unifying Graph Convolutional Neural Networks and Label Propagation

Abstract

Label Propagation (LPA) and Graph Convolutional Neural Networks (GCN) are both message passing algorithms on graphs. Both solve the task of node classification but LPA propagates node label information across the edges of the graph, while GCN propagates and transforms node feature information. However, while conceptually similar, theoretical relation between LPA and GCN has not yet been investigated. Here we study the relationship between LPA and GCN in terms of two aspects: (1) feature/label smoothing where we analyze how the feature/label of one node is spread over its neighbors; And, (2) feature/label influence of how much the initial feature/label of one node influences the final feature/label of another node. Based on our theoretical analysis, we propose an end-to-end model that unifies GCN and LPA for node classification. In our unified model, edge weights are learnable, and the LPA serves as regularization to assist the GCN in learning proper edge weights that lead to improved classification performance. Our model can also be seen as learning attention weights based on node labels, which is more task-oriented than existing feature-based attention models. In a number of experiments on real-world graphs, our model shows superiority over state-of-the-art GCN-based methods in terms of node classification accuracy.

Benchmark Results

Tested on 1 dataset SOTA at publication on 1

Tables show presented results in global context (best 3 papers + GCN + MLP).

Classic

#ModelAccuracy ↑Paper
1
DoG
0.9690 ±0.0030
2
GWN-fa
0.9667 ±0.0026
3
GWN-sym
0.9666 ±0.0026
6
GraphSAGE
actual #6 vs paper #100 94 places worse
0.9593 ±0.0025
best reported
actual #6 vs paper #100 94 places worse
paper 0.9260 ±0.0160
best today: Graph Wave Networks (WWW 2025)
paper 0.9260 ±0.0160 Δ today 0.0333
12
GCN
actual #12 vs paper #36 24 places worse
0.9360 ±0.0150
actual #12 vs paper #36 24 places worse
paper 0.9360 ±0.0150
paper 0.9360 ±0.0150 Δ at pub 0.0233
18
GCN-LPA
0.9480 ±0.0040
This paper
21
GAT
actual #21 vs paper #30 9 places worse
0.9380 ±0.0040
actual #21 vs paper #30 9 places worse
paper 0.9380 ±0.0040
paper 0.9380 ±0.0040 Δ at pub 0.0330
88
MLP
actual #88 vs paper #132 44 places worse
0.9280 ±0.0020
best reported
actual #88 vs paper #132 44 places worse
paper 0.9170 ±0.0140

Difference within reported uncertainty; not counted as underperformance.

paper 0.9170 ±0.0140 Δ today 0.0110
106
JK-Net
0.9240 ±0.0040
This paper
138
GIN
0.9140 ±0.0020
146
LPA
0.9130 ±0.0020
This paper
151
LR
0.9110 ±0.0060
This paper
SOTA performance (not significantly different from the best) Proposed method (this paper) Baseline / comparison (this paper) Global context (other papers) Best at pub — reported value improved over the best known when published Best today — OK at publication; today's leaderboard best is elsewhere