ES-GNN: Generalizing Graph Neural Networks Beyond Homophily with Edge Splitting

Jingwei Guo, Kaizhu Huang, Xinping Yi, Rui Zhang

Main figure for ES-GNN: Generalizing Graph Neural Networks Beyond Homophily with Edge Splitting

Abstract

While Graph Neural Networks (GNNs) have achieved enormous success in multiple graph analytical tasks, modern variants mostly rely on the strong inductive bias of homophily. However, real-world networks typically exhibit both homophilic and heterophilic linking patterns, wherein adjacent nodes may share dissimilar attributes and distinct labels. Therefore, GNNs smoothing node proximity holistically may aggregate both task-relevant and irrelevant (even harmful) information, limiting their ability to generalize to heterophilic graphs and potentially causing non-robustness. In this work, we propose a novel Edge Splitting GNN (ES-GNN) framework to adaptively distinguish between graph edges either relevant or irrelevant to learning tasks. This essentially transfers the original graph into two subgraphs with the same node set but complementary edge sets dynamically. Given that, information propagation separately on these subgraphs and edge splitting are alternatively conducted, thus disentangling the task-relevant and irrelevant features. Theoretically, we show that our ES-GNN can be regarded as a solution to a disentangled graph denoising problem, which further illustrates our motivations and interprets the improved generalization beyond homophily. Extensive experiments over 11 benchmark and 1 synthetic datasets not only demonstrate the effective performance of ES-GNN but also highlight its robustness to adversarial graphs and mitigation of the over-smoothing problem.

Proposed method: ES-GNN

Benchmark Results

Tested on 3 datasets 9 baseline values reported too low

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

Heterophilic Graphs

#ModelAccuracy ↑Paper
1
P^2GNN
0.9672 ±0.0147
2
DoG
0.9660 ±0.0210
3
GPF-plus
0.9583 ±0.0419
5
ACM-GCN
actual #5 vs paper #201 196 places worse
0.9557 ±0.0360
best reported
actual #5 vs paper #201 196 places worse
paper 0.8220 ±0.0590
paper 0.8220 ±0.0590 Δ today 0.1337
30
GPR-GNN
actual #30 vs paper #208 178 places worse
0.9291 ±0.0132
best reported
actual #30 vs paper #208 178 places worse
paper 0.8170 ±0.0490
paper 0.8170 ±0.0490 Δ at pub 0.1121
34
MLP
0.9230 ±0.0070
40
H2GCN
actual #40 vs paper #246 206 places worse
0.9189 ±0.0393
best reported
actual #40 vs paper #246 206 places worse
paper 0.7980 ±0.0730
best at pub: Graph-Coupled Oscillator Networks (ICML 2022)
paper 0.7980 ±0.0730 Δ at pub 0.0510 Δ today 0.1209
53
GraphSAGE
0.9000 ±0.0365
61
FAGCN
actual #61 vs paper #239 178 places worse
0.8961 ±0.0152
best reported
actual #61 vs paper #239 178 places worse
paper 0.8030 ±0.0550
paper 0.8030 ±0.0550 Δ at pub 0.0213 Δ today 0.0931
104
WRGAT
actual #104 vs paper #237 133 places worse
0.8698
best reported
actual #104 vs paper #237 133 places worse
paper 0.8050 ±0.0610

Difference within reported uncertainty; not counted as underperformance.

paper 0.8050 ±0.0610 Δ today 0.0648
141
GloGNN
actual #141 vs paper #216 75 places worse
0.8524 ±0.0490
best reported
actual #141 vs paper #216 75 places worse
paper 0.8140 ±0.0560

Difference within reported uncertainty; not counted as underperformance.

paper 0.8140 ±0.0560 Δ at pub 0.0292 Δ today 0.0384
175
GOAL
actual #175 vs paper #371 196 places worse
0.8362 ±0.0670
best reported
actual #175 vs paper #371 196 places worse
paper 0.7200 ±0.0740

Difference within reported uncertainty; not counted as underperformance.

paper 0.7200 ±0.0740 Δ today 0.1162
198
ES-GNN
0.8230 ±0.0570
This paper
211
GAT
actual #211 vs paper #564 353 places worse
0.8162 ±0.0645
best reported
actual #211 vs paper #564 353 places worse
paper 0.5540 ±0.0590
best at pub: Graph Pointer Neural Networks (AAAI 2021)
paper 0.5540 ±0.0590 Δ at pub 0.0405 Δ today 0.2622
257
GCN
actual #257 vs paper #480 223 places worse
0.7933 ±0.0447
best reported
actual #257 vs paper #480 223 places worse
paper 0.6170 ±0.0370
best today: Graph Wave Networks (WWW 2025)
paper 0.6170 ±0.0370 Δ at pub 0.1527 Δ today 0.1763
273
GEN
0.7830 ±0.0800
This paper
330
SGC
actual #330 vs paper #576 246 places worse
0.7440 ±0.0600
best reported
actual #330 vs paper #576 246 places worse
paper 0.5140 ±0.0220
379
DisenGCN
0.7130 ±0.0570
This paper
398
FactorGCN
0.6950 ±0.0650
This paper
429
NeuralSparse
0.6640 ±0.0570
This paper
489
GCN-LPA
0.6120 ±0.0760
This paper
496
DisGNN
0.6060 ±0.0390
This paper
562
VEPM
0.5580 ±0.0430
This paper
#ModelAccuracy ↑Paper
1
P^2GNN
0.9541 ±0.0272
2
ACM-GCN
actual #2 vs paper #155 153 places worse
0.9480 ±0.0380
best reported
actual #2 vs paper #155 153 places worse
paper 0.8210 ±0.0490
best today: Heterophily-informed Message Passing (TMLR 2025)
paper 0.8210 ±0.0490 Δ today 0.1270
3
RF-GCN
0.9429
11
GPR-GNN
actual #11 vs paper #182 171 places worse
0.9279 ±0.0312
best reported
actual #11 vs paper #182 171 places worse
paper 0.7990 ±0.0530
paper 0.7990 ±0.0530 Δ at pub 0.1167 Δ today 0.1289
24
MLP
0.9136 ±0.0070
38
FAGCN
actual #38 vs paper #183 145 places worse
0.7940 ±0.0550
actual #38 vs paper #183 145 places worse
paper 0.7940 ±0.0550

Improvement within reported uncertainty; not highlighted.

paper 0.7940 ±0.0550 Δ at pub 0.0021 Δ today 0.0912
68
H2GCN
actual #68 vs paper #182 114 places worse
0.8623 ±0.0471
best reported
actual #68 vs paper #182 114 places worse
paper 0.7960 ±0.0490
best at pub: Graph-Coupled Oscillator Networks (ICML 2022)

Difference within reported uncertainty; not counted as underperformance.

paper 0.7960 ±0.0490 Δ at pub 0.0310 Δ today 0.0663
74
GloGNN
actual #74 vs paper #155 81 places worse
0.8595 ±0.0510
best reported
actual #74 vs paper #155 81 places worse
paper 0.8200 ±0.0350

Difference within reported uncertainty; not counted as underperformance.

paper 0.8200 ±0.0350 Δ at pub 0.0151 Δ today 0.0395
81
GOAL
actual #81 vs paper #428 347 places worse
0.8568 ±0.0620
best reported
actual #81 vs paper #428 347 places worse
paper 0.5490 ±0.0660
138
SAGE
0.8269
150
ES-GNN
0.8220 ±0.0400
This paper
158
GAT
actual #158 vs paper #484 326 places worse
0.8190 ±0.0540
best reported
actual #158 vs paper #484 326 places worse
paper 0.5040 ±0.0590
best at pub: Graph-Coupled Oscillator Networks (ICML 2022)
paper 0.5040 ±0.0590 Δ at pub 0.1150 Δ today 0.3150
160
WRGAT
actual #160 vs paper #185 25 places worse
0.8162 ±0.0390
best reported
actual #160 vs paper #185 25 places worse
paper 0.7920 ±0.0350

Difference within reported uncertainty; not counted as underperformance.

paper 0.7920 ±0.0350 Δ at pub 0.0242 Δ today 0.0242
168
GEN
0.8100 ±0.0390
This paper
170
GCN
actual #170 vs paper #456 286 places worse
0.8082 ±0.0360
best reported
actual #170 vs paper #456 286 places worse
paper 0.5280 ±0.0600
paper 0.5280 ±0.0600 Δ at pub 0.1298 Δ today 0.2802
211
DisenGCN
0.7740 ±0.0440
This paper
252
SGC
actual #252 vs paper #474 222 places worse
0.7350 ±0.0430
best reported
actual #252 vs paper #474 222 places worse
paper 0.5120 ±0.0090
324
GCN-LPA
0.6560 ±0.0730
This paper
343
NeuralSparse
0.6410 ±0.0550
This paper
467
DisGNN
0.5200 ±0.0570
This paper
475
VEPM
0.5120 ±0.0700
This paper
482
FactorGCN
0.5060 ±0.0180
This paper
#ModelAccuracy ↑Paper
1
DiGGR
0.4535 ±0.0353
2
TRIGON
0.4402 ±0.0028
3
DoG
0.4320 ±0.0120
16
ACM-GCN
actual #16 vs paper #156 140 places worse
0.4198 ±0.0089
best reported
actual #16 vs paper #156 140 places worse
paper 0.3660 ±0.0100
paper 0.3660 ±0.0100 Δ today 0.0538
42
MLP
0.4026 ±0.0108
53
GPR-GNN
actual #53 vs paper #89 36 places worse
0.3992 ±0.0067
best reported
actual #53 vs paper #89 36 places worse
paper 0.3800 ±0.0110
paper 0.3800 ±0.0110 Δ at pub 0.0191 Δ today 0.0192
56
FAGCN
actual #56 vs paper #93 37 places worse
0.3970
best reported
actual #56 vs paper #93 37 places worse
paper 0.3790 ±0.0100
paper 0.3790 ±0.0100 Δ at pub 0.0180
58
GloGNN
actual #58 vs paper #83 25 places worse
0.3820 ±0.0120
actual #58 vs paper #83 25 places worse
paper 0.3820 ±0.0120

Improvement within reported uncertainty; not highlighted.

paper 0.3820 ±0.0120 Δ at pub 0.0085
68
GraphSAGE
0.3899 ±0.0085
69
ES-GNN
0.3890 ±0.0080
This paper
71
H2GCN
actual #71 vs paper #81 10 places worse
0.3840 ±0.0100
actual #71 vs paper #81 10 places worse
paper 0.3840 ±0.0100
paper 0.3840 ±0.0100 Δ at pub 0.0254
75
WRGAT
actual #75 vs paper #75
0.3860 ±0.0110
actual #75 vs paper #75
paper 0.3860 ±0.0110
paper 0.3860 ±0.0110 Δ at pub 0.0207
104
GCN-LPA
0.3780 ±0.0090
This paper
119
GEN
0.3730 ±0.0140
This paper
135
GCN
actual #135 vs paper #322 187 places worse
0.3690
best reported
actual #135 vs paper #322 187 places worse
paper 0.3120 ±0.0130
paper 0.3120 ±0.0130 Δ at pub 0.0570
150
DisenGCN
0.3670 ±0.0120
This paper
163
GOAL
actual #163 vs paper #171 8 places worse
0.3646 ±0.0100
best reported
actual #163 vs paper #171 8 places worse
paper 0.3630 ±0.0100

Difference within reported uncertainty; not counted as underperformance.

paper 0.3630 ±0.0100 Δ today 0.0016
182
GAT
actual #182 vs paper #336 154 places worse
0.3050 ±0.0120
actual #182 vs paper #336 154 places worse
paper 0.3050 ±0.0120
prev best: Graph Pointer Neural Networks (AAAI 2021)

Improvement within reported uncertainty; not highlighted.

paper 0.3050 ±0.0120 Δ at pub 0.0076 Δ today 0.0555
212
NeuralSparse
0.3550 ±0.0110
This paper
237
SGC
actual #237 vs paper #328 91 places worse
0.3090 ±0.0060
actual #237 vs paper #328 91 places worse
paper 0.3090 ±0.0060
346
DisGNN
0.3020 ±0.0130
This paper
365
VEPM
0.2930 ±0.0110
This paper
372
FactorGCN
0.2900 ±0.0140
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 result worse than the best known when published (best reported in green) Best at pub — reported value improved over the best known when published Improved at pub — later paper surpassed this result Best today — OK at publication; today's leaderboard best is elsewhere