Graph Homophily Booster: Rethinking the Role of Discrete Features on Heterophilic Graphs

Ruizhong Qiu, Ting-Wei Li, Gaotang Li, Hanghang Tong

Main figure for Graph Homophily Booster: Rethinking the Role of Discrete Features on Heterophilic Graphs

Abstract

Graph neural networks (GNNs) have emerged as a powerful tool for modeling graph-structured data, demonstrating remarkable success in many real-world applications such as complex biological network analysis, neuroscientific analysis, and social network analysis. However, existing GNNs often struggle with heterophilic graphs, where connected nodes tend to have dissimilar features or labels. While numerous methods have been proposed to address this challenge, they primarily focus on architectural designs without directly targeting the root cause of the heterophily problem. These approaches still perform even worse than the simplest MLPs on challenging heterophilic datasets. For instance, our experiments show that 21 latest GNNs still fall behind the MLP on the Actor dataset. This critical challenge calls for an innovative approach to addressing graph heterophily beyond architectural designs. To bridge this gap, we propose and study a new and unexplored paradigm: directly increasing the graph homophily via a carefully designed graph transformation. In this work, we present a simple yet effective framework called ph homo ly boos r (GRAPHITE) to address graph heterophily. To the best of our knowledge, this work is the first method that explicitly transforms the graph to directly improve the graph homophily. Stemmed from the exact definition of homophily, our proposed GRAPHITE creates feature nodes to facilitate homophilic message passing between nodes that share similar features. Furthermore, we both theoretically and empirically show that our proposed GRAPHITE significantly increases the homophily of originally heterophilic graphs, with only a slight increase in the graph size. Extensive experiments on challenging datasets demonstrate that our proposed GRAPHITE significantly outperforms state-of-the-art methods on heterophilic graphs while achieving comparable accuracy with state-of-the-art methods on homophilic graphs. Furthermore, our proposed graph transformation alone can already enhance the performance of homophilic GNNs on heterophilic graphs, even though they were not originally designed for heterophilic graphs. We will release our code upon the publication of this paper.

Proposed method: Graphite

Benchmark Results

Tested on 4 datasets 61 baseline values reported too low

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

Heterophilic Graphs

#ModelAccuracy ↑Paper
1
DiGGR
0.4535 ±0.0353
2
TRIGON
0.4402 ±0.0028
3
DoG
0.4320 ±0.0120
23
SGFormer
actual #23 vs paper #420 397 places worse
0.4169 ±0.0063
best reported
actual #23 vs paper #420 397 places worse
paper 0.2589 ±0.0080
paper 0.2589 ±0.0080 Δ at pub 0.1580
38
GCNII
actual #38 vs paper #240 202 places worse
0.4082 ±0.0179
best reported
actual #38 vs paper #240 202 places worse
paper 0.3478 ±0.0150
paper 0.3478 ±0.0150 Δ at pub 0.0383 Δ today 0.0604
41
APPNP
actual #41 vs paper #277 236 places worse
0.4046 ±0.0064
best reported
actual #41 vs paper #277 236 places worse
paper 0.3368 ±0.0126
paper 0.3368 ±0.0126 Δ at pub 0.0678
42
MLP
actual #42 vs paper #234 192 places worse
0.4026 ±0.0108
best reported
actual #42 vs paper #234 192 places worse
paper 0.3504 ±0.0153
paper 0.3504 ±0.0153 Δ at pub 0.0522
52
GPRGNN
actual #52 vs paper #214 162 places worse
0.3992 ±0.0067
best reported
actual #52 vs paper #214 162 places worse
paper 0.3542 ±0.0133
paper 0.3542 ±0.0133 Δ at pub 0.0450 Δ today 0.0450
56
FAGCN
actual #56 vs paper #177 121 places worse
0.3970
best reported
actual #56 vs paper #177 121 places worse
paper 0.3618 ±0.0152
paper 0.3618 ±0.0152 Δ at pub 0.0352
58
GloGNN
actual #58 vs paper #488 430 places worse
0.3959 ±0.0029
best reported
actual #58 vs paper #488 430 places worse
paper 0.1980 ±0.0261
paper 0.1980 ±0.0261 Δ at pub 0.1979
62
GGCN
actual #62 vs paper #291 229 places worse
0.3929 ±0.0048
best reported
actual #62 vs paper #291 229 places worse
paper 0.3276 ±0.0139
paper 0.3276 ±0.0139 Δ at pub 0.0505 Δ today 0.0653
68
GraphSAGE
actual #68 vs paper #235 167 places worse
0.3899 ±0.0085
best reported
actual #68 vs paper #235 167 places worse
paper 0.3495 ±0.0106
paper 0.3495 ±0.0106 Δ at pub 0.0404
71
H2GCN
actual #71 vs paper #258 187 places worse
0.3885 ±0.0117
best reported
actual #71 vs paper #258 187 places worse
paper 0.3420 ±0.0147
paper 0.3420 ±0.0147 Δ at pub 0.0420 Δ today 0.0465
88
ChebNet
actual #88 vs paper #254 166 places worse
0.3802 ±0.0023
best reported
actual #88 vs paper #254 166 places worse
paper 0.3440 ±0.0118
paper 0.3440 ±0.0118 Δ at pub 0.0362
109
Graphite
0.3769 ±0.0157
This paper
135
GCN
actual #135 vs paper #345 210 places worse
0.3690
best reported
actual #135 vs paper #345 210 places worse
paper 0.3021 ±0.0086
paper 0.3021 ±0.0086 Δ at pub 0.0669
136
NodeFormer
actual #136 vs paper #366 230 places worse
0.3690 ±0.0100
best reported
actual #136 vs paper #366 230 places worse
paper 0.2926 ±0.0231
best at pub: Even Sparser Graph Transformers (NeurIPS 2024)
paper 0.2926 ±0.0231 Δ at pub 0.0764
141
DIFFormer
actual #141 vs paper #417 276 places worse
0.3682 ±0.0110
best reported
actual #141 vs paper #417 276 places worse
paper 0.2631 ±0.0119
paper 0.2631 ±0.0119 Δ at pub 0.1051 Δ today 0.1051
162
MixHop
actual #162 vs paper #217 55 places worse
0.3648 ±0.0120
best reported
actual #162 vs paper #217 55 places worse
paper 0.3540 ±0.0134

Difference within reported uncertainty; not counted as underperformance.

paper 0.3540 ±0.0134 Δ at pub 0.0108
182
GAT
actual #182 vs paper #376 194 places worse
0.3605 ±0.0035
best reported
actual #182 vs paper #376 194 places worse
paper 0.2886 ±0.0099
paper 0.2886 ±0.0099 Δ at pub 0.0719
200
OrderedGNN
0.3564 ±0.0098
This paper
211
DAGNN
actual #211 vs paper #284 73 places worse
0.3551 ±0.0110
best reported
actual #211 vs paper #284 73 places worse
paper 0.3315 ±0.0114
230
GATv2
actual #230 vs paper #376 146 places worse
0.3510 ±0.0020
best reported
actual #230 vs paper #376 146 places worse
paper 0.2887 ±0.0139
paper 0.2887 ±0.0139 Δ at pub 0.0623
236
TAGCN
0.3492 ±0.0119
This paper
237
SGC
actual #237 vs paper #366 129 places worse
0.3490 ±0.0070
best reported
actual #237 vs paper #366 129 places worse
paper 0.2926 ±0.0141
paper 0.2926 ±0.0141 Δ at pub 0.0564
266
GIN
actual #266 vs paper #389 123 places worse
0.3410 ±0.0030
best reported
actual #266 vs paper #389 123 places worse
paper 0.2829 ±0.0145
paper 0.2829 ±0.0145 Δ at pub 0.0581
281
JKNet
actual #281 vs paper #382 101 places worse
0.3342 ±0.0028
best reported
actual #281 vs paper #382 101 places worse
paper 0.2863 ±0.0094
paper 0.2863 ±0.0094 Δ at pub 0.0479
286
ALT
0.3310 ±0.0138
This paper
333
Virtual Node
0.3071 ±0.0082
This paper
#ModelAccuracy ↑Paper
1
Hetero-S (GAT 8-layer)
0.8693
2
Dir-GNN+CNA
0.8586 ±0.0180
3
GAT
actual #3 vs paper #254 251 places worse
0.8560
best reported
actual #3 vs paper #254 251 places worse
paper 0.4011 ±0.0280
paper 0.4011 ±0.0280 Δ at pub 0.4549
32
JKNet
actual #32 vs paper #252 220 places worse
0.7419
best reported
actual #32 vs paper #252 220 places worse
paper 0.4039 ±0.0485
paper 0.4039 ±0.0485 Δ at pub 0.3380
45
GloGNN
actual #45 vs paper #254 209 places worse
0.7133 ±0.0242
best reported
actual #45 vs paper #254 209 places worse
paper 0.4017 ±0.0466
paper 0.4017 ±0.0466 Δ at pub 0.3104 Δ today 0.3116
48
GGCN
actual #48 vs paper #269 221 places worse
0.7114 ±0.0184
best reported
actual #48 vs paper #269 221 places worse
paper 0.3408 ±0.0344
paper 0.3408 ±0.0344 Δ at pub 0.3706 Δ today 0.3706
52
GCN
actual #52 vs paper #254 202 places worse
0.7033
best reported
actual #52 vs paper #254 202 places worse
paper 0.4006 ±0.0438
paper 0.4006 ±0.0438 Δ at pub 0.3027
72
GPRGNN
actual #72 vs paper #251 179 places worse
0.6748 ±0.0040
best reported
actual #72 vs paper #251 179 places worse
paper 0.4050 ±0.0455
paper 0.4050 ±0.0455 Δ at pub 0.2678 Δ today 0.2698
76
SGC
actual #76 vs paper #247 171 places worse
0.6710 ±0.0290
best reported
actual #76 vs paper #247 171 places worse
paper 0.4140 ±0.0491
paper 0.4140 ±0.0491 Δ at pub 0.2570
79
APPNP
actual #79 vs paper #263 184 places worse
0.6670 ±0.0270
best reported
actual #79 vs paper #263 184 places worse
paper 0.3793 ±0.0433
paper 0.3793 ±0.0433 Δ at pub 0.2877
103
GCNII
actual #103 vs paper #246 143 places worse
0.6386 ±0.0304
best reported
actual #103 vs paper #246 143 places worse
paper 0.4156 ±0.0274
paper 0.4156 ±0.0274 Δ at pub 0.2230 Δ today 0.2230
107
FAGCN
actual #107 vs paper #255 148 places worse
0.6344 ±0.0205
best reported
actual #107 vs paper #255 148 places worse
paper 0.3983 ±0.0393
108
SAGE
0.6340 ±0.0300
115
GraphSAGE
actual #115 vs paper #257 142 places worse
0.6215 ±0.0042
best reported
actual #115 vs paper #257 142 places worse
paper 0.3933 ±0.0453
paper 0.3933 ±0.0453 Δ at pub 0.2282
129
MixHop
actual #129 vs paper #263 134 places worse
0.6050 ±0.0253
best reported
actual #129 vs paper #263 134 places worse
paper 0.3793 ±0.0387
paper 0.3793 ±0.0387 Δ at pub 0.2257 Δ today 0.2257
133
H2GCN
actual #133 vs paper #251 118 places worse
0.6030 ±0.0231
best reported
actual #133 vs paper #251 118 places worse
paper 0.4089 ±0.0313
paper 0.4089 ±0.0313 Δ at pub 0.1941
140
ChebNet
actual #140 vs paper #269 129 places worse
0.5928 ±0.0125
best reported
actual #140 vs paper #269 129 places worse
paper 0.3430 ±0.0433
paper 0.3430 ±0.0433 Δ at pub 0.2498
169
MLP
actual #169 vs paper #262 93 places worse
0.5429
best reported
actual #169 vs paper #262 93 places worse
paper 0.3844 ±0.0514
paper 0.3844 ±0.0514 Δ at pub 0.1585
188
SGFormer
actual #188 vs paper #240 52 places worse
0.5140 ±0.0170
best reported
actual #188 vs paper #240 52 places worse
paper 0.4279 ±0.0406
paper 0.4279 ±0.0406 Δ at pub 0.0861
214
GATv2
actual #214 vs paper #256 42 places worse
0.4710 ±0.0030
best reported
actual #214 vs paper #256 42 places worse
paper 0.3972 ±0.0660

Difference within reported uncertainty; not counted as underperformance.

paper 0.3972 ±0.0660 Δ at pub 0.0738
219
GIN
actual #219 vs paper #254 35 places worse
0.4610 ±0.0040
best reported
actual #219 vs paper #254 35 places worse
paper 0.4017 ±0.0476

Difference within reported uncertainty; not counted as underperformance.

paper 0.4017 ±0.0476 Δ at pub 0.0593 Δ today 0.0593
223
DAGNN
actual #223 vs paper #259 36 places worse
0.4592 ±0.0230
best reported
actual #223 vs paper #259 36 places worse
paper 0.3894 ±0.0353
227
Graphite
0.4508 ±0.0404
This paper
247
Virtual Node
0.4145 ±0.0546
This paper
250
TAGCN
0.4101 ±0.0377
This paper
257
ALT
0.3961 ±0.0336
This paper
258
DIFFormer
0.3916 ±0.0410
This paper
263
OrderedGNN
0.3838 ±0.0365
This paper
267
NodeFormer
actual #267 vs paper #268 1 place worse
0.3492 ±0.0408
actual #267 vs paper #268 1 place worse
paper 0.3492 ±0.0408

Improvement within reported uncertainty; not highlighted.

paper 0.3492 ±0.0408 Δ at pub 0.0014
#ModelAccuracy ↑Paper
1
IBG-NN
0.7763 ±0.0179
2
Dir-GNN+CNA
0.7747 ±0.0128
3
DHGNN
0.7684 ±0.0161
19
GloGNN
actual #19 vs paper #243 224 places worse
0.7121 ±0.0184
best reported
actual #19 vs paper #243 224 places worse
paper 0.2872 ±0.0263
paper 0.2872 ±0.0263 Δ at pub 0.4249
39
H2GCN
actual #39 vs paper #228 189 places worse
0.6190 ±0.0140
best reported
actual #39 vs paper #228 189 places worse
paper 0.3402 ±0.0315
paper 0.3402 ±0.0315 Δ at pub 0.2788
46
GCN
actual #46 vs paper #212 166 places worse
0.6067
best reported
actual #46 vs paper #212 166 places worse
paper 0.3557 ±0.0186
paper 0.3557 ±0.0186 Δ at pub 0.2510
67
GAT
actual #67 vs paper #231 164 places worse
0.5630 ±0.0220
best reported
actual #67 vs paper #231 164 places worse
paper 0.3274 ±0.0302
paper 0.3274 ±0.0302 Δ at pub 0.2356
68
APPNP
actual #68 vs paper #229 161 places worse
0.5590 ±0.0290
best reported
actual #68 vs paper #229 161 places worse
paper 0.3375 ±0.0231
paper 0.3375 ±0.0231 Δ at pub 0.2215
69
GGCN
actual #69 vs paper #219 150 places worse
0.5567 ±0.0187
best reported
actual #69 vs paper #219 150 places worse
paper 0.3506 ±0.0565
paper 0.3506 ±0.0565 Δ at pub 0.2011 Δ today 0.2061
76
GPRGNN
actual #76 vs paper #220 144 places worse
0.5435 ±0.0087
best reported
actual #76 vs paper #220 144 places worse
paper 0.3497 ±0.0283
paper 0.3497 ±0.0283 Δ at pub 0.1938
81
SGC
actual #81 vs paper #181 100 places worse
0.5230 ±0.0230
best reported
actual #81 vs paper #181 100 places worse
paper 0.3827 ±0.0216
paper 0.3827 ±0.0216 Δ at pub 0.1403
120
SAGE
0.4460 ±0.0130
125
ChebNet
actual #125 vs paper #233 108 places worse
0.4386 ±0.0164
best reported
actual #125 vs paper #233 108 places worse
paper 0.3175 ±0.0342
paper 0.3175 ±0.0342 Δ at pub 0.1211
127
MixHop
actual #127 vs paper #240 113 places worse
0.4380 ±0.0148
best reported
actual #127 vs paper #240 113 places worse
paper 0.3043 ±0.0233
paper 0.3043 ±0.0233 Δ at pub 0.1337 Δ today 0.1337
128
GraphSAGE
actual #128 vs paper #227 99 places worse
0.4378 ±0.0190
best reported
actual #128 vs paper #227 99 places worse
paper 0.3443 ±0.0268
131
Graphite
0.4306 ±0.0289
This paper
138
SGFormer
actual #138 vs paper #225 87 places worse
0.4265 ±0.0241
best reported
actual #138 vs paper #225 87 places worse
paper 0.3454 ±0.0296
139
FAGCN
actual #139 vs paper #201 62 places worse
0.4259 ±0.0069
best reported
actual #139 vs paper #201 62 places worse
paper 0.3652 ±0.0172
156
JKNet
actual #156 vs paper #156
0.4081 ±0.0260
actual #156 vs paper #156
paper 0.4081 ±0.0260
paper 0.4081 ±0.0260 Δ at pub 0.0998
169
GIN
actual #169 vs paper #169
0.3951 ±0.0283
actual #169 vs paper #169
paper 0.3951 ±0.0283
paper 0.3951 ±0.0283 Δ at pub 0.0491
172
MLP
actual #172 vs paper #229 57 places worse
0.3930 ±0.0079
best reported
actual #172 vs paper #229 57 places worse
paper 0.3391 ±0.0155
paper 0.3391 ±0.0155 Δ at pub 0.0272 Δ today 0.0539
175
NodeFormer
actual #175 vs paper #266 91 places worse
0.3889 ±0.0267
best reported
actual #175 vs paper #266 91 places worse
paper 0.2429 ±0.0260
176
GCNII
actual #176 vs paper #205 29 places worse
0.3881 ±0.0197
best reported
actual #176 vs paper #205 29 places worse
paper 0.3593 ±0.0287

Difference within reported uncertainty; not counted as underperformance.

paper 0.3593 ±0.0287 Δ at pub 0.0254 Δ today 0.0288
184
Virtual Node
0.3800 ±0.0228
This paper
197
ALT
0.3728 ±0.0149
This paper
218
GATv2
actual #218 vs paper #232 14 places worse
0.3510 ±0.0020
best reported
actual #218 vs paper #232 14 places worse
paper 0.3249 ±0.0251

Difference within reported uncertainty; not counted as underperformance.

paper 0.3249 ±0.0251 Δ at pub 0.0261
223
DAGNN
actual #223 vs paper #223
0.3472 ±0.0255
actual #223 vs paper #223
paper 0.3472 ±0.0255
230
TAGCN
0.3333 ±0.0237
This paper
231
DIFFormer
0.3317 ±0.0284
This paper
232
OrderedGNN
0.3270 ±0.0242
This paper

Heterophily Benchmark

#ModelROC-AUC ↑Paper
1
BuNN
0.9899 ±0.0016
2
DC-GNN
0.9850 ±0.0021
3
Tango -GPS
0.9839 ±0.0054
20
Graphite
0.9478 ±0.0041
This paper
36
GAT
actual #36 vs paper #104 68 places worse
0.9391 ±0.0035
best reported
actual #36 vs paper #104 68 places worse
paper 0.8759 ±0.0135
paper 0.8759 ±0.0135 Δ at pub 0.0479 Δ today 0.0632
42
GraphSAGE
actual #42 vs paper #80 38 places worse
0.9358 ±0.0005
best reported
actual #42 vs paper #80 38 places worse
paper 0.9054 ±0.0066
paper 0.9054 ±0.0066 Δ at pub 0.0304
46
SAGE
0.9351 ±0.0057
66
ChebNet
0.9160 ±0.0044
This paper
67
TAGCN
0.9154 ±0.0056
This paper
68
GCN
actual #68 vs paper #134 66 places worse
0.9150 ±0.0006
best reported
actual #68 vs paper #134 66 places worse
paper 0.7232 ±0.0093
paper 0.7232 ±0.0093 Δ at pub 0.1918
73
OrderedGNN
actual #73 vs paper #73
0.9101 ±0.0050
actual #73 vs paper #73
paper 0.9101 ±0.0050
paper 0.9101 ±0.0050 Δ at pub 0.1043
75
DIFFormer
actual #75 vs paper #141 66 places worse
0.9089 ±0.0058
best reported
actual #75 vs paper #141 66 places worse
paper 0.6925 ±0.0093
paper 0.6925 ±0.0093 Δ at pub 0.2164 Δ today 0.2164
85
H2GCN
actual #85 vs paper #106 21 places worse
0.8995 ±0.0038
best reported
actual #85 vs paper #106 21 places worse
paper 0.8708 ±0.0082
paper 0.8708 ±0.0082 Δ at pub 0.0287
91
FAGCN
actual #91 vs paper #111 20 places worse
0.8969 ±0.0060
best reported
actual #91 vs paper #111 20 places worse
paper 0.8469 ±0.0205
paper 0.8469 ±0.0205 Δ at pub 0.0500
92
MixHop
0.8968 ±0.0057
This paper
96
ALT
0.8906 ±0.0064
This paper
100
GATv2
0.8885 ±0.0116
This paper
102
SGFormer
actual #102 vs paper #155 53 places worse
0.8860 ±0.0049
best reported
actual #102 vs paper #155 53 places worse
paper 0.5206 ±0.0050
paper 0.5206 ±0.0050 Δ today 0.3654
103
GCNII
0.8842 ±0.0085
This paper
104
GIN
actual #104 vs paper #125 21 places worse
0.8782 ±0.0034
best reported
actual #104 vs paper #125 21 places worse
paper 0.7589 ±0.0209
paper 0.7589 ±0.0209 Δ at pub 0.1193
105
GGCN
actual #105 vs paper #111 6 places worse
0.8754 ±0.0122
best reported
actual #105 vs paper #111 6 places worse
paper 0.8476 ±0.0184
paper 0.8476 ±0.0184 Δ at pub 0.0278
108
NodeFormer
actual #108 vs paper #122 14 places worse
0.8671 ±0.0088
best reported
actual #108 vs paper #122 14 places worse
paper 0.7771 ±0.0350
paper 0.7771 ±0.0350 Δ at pub 0.0900 Δ today 0.0900
109
GPRGNN
actual #109 vs paper #113 4 places worse
0.8624 ±0.0061
best reported
actual #109 vs paper #113 4 places worse
paper 0.8394 ±0.0098
paper 0.8394 ±0.0098 Δ today 0.0230
119
JKNet
0.8100 ±0.0092
This paper
134
Virtual Node
0.7236 ±0.0098
This paper
135
SGC
0.7211 ±0.0095
This paper
143
DAGNN
0.6787 ±0.0126
This paper
144
APPNP
0.6736 ±0.0108
This paper
148
GloGNN
actual #148 vs paper #154 6 places worse
0.6253 ±0.0134
best reported
actual #148 vs paper #154 6 places worse
paper 0.5342 ±0.0147
paper 0.5342 ±0.0147 Δ at pub 0.0911
156
MLP
actual #156 vs paper #156
0.5099 ±0.0147
actual #156 vs paper #156
paper 0.5099 ±0.0147
prev best: Evolving Computation Graphs (ICML 2023)

Improvement within reported uncertainty; not highlighted.

paper 0.5099 ±0.0147 Δ at pub 0.0010
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 Best today — OK at publication; today's leaderboard best is elsewhere