Simple Graph Condensation

Zhenbang Xiao, Yu Wang, Shunyu Liu, Huiqiong Wang, Mingli Song, Tongya Zheng

Main figure for Simple Graph Condensation

Abstract

The burdensome training costs on large-scale graphs have aroused significant interest in graph condensation, which involves tuning Graph Neural Networks (GNNs) on a small condensed graph for use on the large-scale original graph. Existing methods primarily focus on aligning key metrics between the condensed and original graphs, such as gradients, output distribution and trajectories of GNNs, satisfactory performance on downstream tasks. However, these complex metrics necessitate intricate external parameters and can potentially disrupt the optimization process of the condensation graph, making the condensation process highly demanding and unstable. This straightforward yet effective strategy achieves a significant speedup of up to 10 times compared to existing graph condensation methods while performing on par with state-of-the-art baselines. Comprehensive experiments conducted on seven benchmark datasets demonstrate the effectiveness of SimGC in prediction accuracy, condensation time, and generalization capability. Our code is available at.

Proposed method: SimGC

Benchmark Results

Tested on 4 datasets 6 baseline values reported too low Non-standard metric on 1 dataset

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

Classic

#ModelAccuracy ↑Paper
1
GraphSAGE+CNA
0.9418 ±0.0033
2
GCN+CNA
0.9366 ±0.0048
3
TransformerConv
0.9350 ±0.0058
21
GCN
0.9004
522
SimGC
0.8210 ±0.0130
This paper
523
Random
actual #523 vs paper #741 218 places worse
0.8209 ±0.0008
best reported
actual #523 vs paper #741 218 places worse
paper 0.7680 ±0.0010
paper 0.7680 ±0.0010 Δ at pub 0.0529
560
SFGC
0.8170 ±0.0050
This paper
615
GCond
actual #615 vs paper #654 39 places worse
0.8090 ±0.0320
best reported
actual #615 vs paper #654 39 places worse
paper 0.8010 ±0.0060

Difference within reported uncertainty; not counted as underperformance.

paper 0.8010 ±0.0060 Δ today 0.0080
629
SGDD
0.8060 ±0.0080
This paper
683
GCDM
0.7940 ±0.0010
This paper
724
MLP
0.7768
742
Herding
0.7680 ±0.0010
This paper
743
K-Center
0.7670 ±0.0010
This paper
#ModelAccuracy ↑Paper
1
CNA
0.9575 ±0.0058
2
IS-GIB
0.9390 ±0.0187
3
EERM
0.9112 ±0.0145
44
GCN
0.8033 ±0.0088
244
SimGC
0.7380 ±0.0250
This paper
350
MLP
0.7289 ±0.0010
415
SFGC
actual #415 vs paper #415
0.7240 ±0.0040
actual #415 vs paper #415
paper 0.7240 ±0.0040
paper 0.7240 ±0.0040 Δ at pub 0.0100
487
Whole Dataset
0.7170 ±0.0010
This paper
572
GCond
actual #572 vs paper #584 12 places worse
0.7080 ±0.0450
best reported
actual #572 vs paper #584 12 places worse
paper 0.7060 ±0.0090

Difference within reported uncertainty; not counted as underperformance.

paper 0.7060 ±0.0090 Δ today 0.0020
593
Random
actual #593 vs paper #648 55 places worse
0.7049 ±0.0008
best reported
actual #593 vs paper #648 55 places worse
paper 0.6910 ±0.0010
paper 0.6910 ±0.0010 Δ at pub 0.0139
606
SGDD
0.7030 ±0.0170
This paper
632
GCDM
0.6980 ±0.0020
This paper
650
K-Center
actual #650 vs paper #650
0.6910 ±0.0010
actual #650 vs paper #650
paper 0.6910 ±0.0010
paper 0.6910 ±0.0010 Δ at pub 0.1670
651
Herding
actual #651 vs paper #651
0.6900 ±0.0010
actual #651 vs paper #651
paper 0.6900 ±0.0010
paper 0.6900 ±0.0010 Δ at pub 0.1190

Reddit

Global leaderboard →
Non-default metric. This paper reports Accuracy; the dataset default is F1. Values below use Accuracy only.

Sorted by Accuracy. Highlighted rows are from other papers.

#ModelAccuracy ↑Paper
1
GAP-EDP
0.9870 ±0.0003
2
NE-ASGCN
0.9758 ±0.0027
3
HSGT
0.9730 ±0.0024
21
GraphSAGE
0.9653 ±0.0011
89
Whole Dataset
0.9350 ±0.0010
This paper
105
SGDD
actual #105 vs paper #140 35 places worse
0.9180 ±0.0190
best reported
actual #105 vs paper #140 35 places worse
paper 0.8670 ±0.0080
paper 0.8670 ±0.0080 Δ at pub 0.0510
110
SimGC
0.9140 ±0.0020
This paper
113
Random
actual #113 vs paper #154 41 places worse
0.9110
best reported
actual #113 vs paper #154 41 places worse
paper 0.6550 ±0.0250
120
GCond
actual #120 vs paper #146 26 places worse
0.9030 ±0.0310
best reported
actual #120 vs paper #146 26 places worse
paper 0.8240 ±0.0100
paper 0.8240 ±0.0100 Δ at pub 0.0723 Δ today 0.0790
124
GCDM
actual #124 vs paper #148 24 places worse
0.8970 ±0.0020
best reported
actual #124 vs paper #148 24 places worse
paper 0.8080 ±0.0310
125
SFGC
actual #125 vs paper #133 8 places worse
0.8970 ±0.0020
best reported
actual #125 vs paper #133 8 places worse
paper 0.8860 ±0.0110

Difference within reported uncertainty; not counted as underperformance.

paper 0.8860 ±0.0110 Δ at pub 0.0110 Δ today 0.0110
147
MLP
0.8240 ±0.0010
153
Herding
0.7140 ±0.0160
This paper
161
K-Center
0.5740 ±0.0180
This paper

OGB

#ModelAccuracy ↑Paper
1
Jacobi
0.8968
2
GPR
0.8953
3
LEMP4HG
0.8939
4
SAGE
0.8933
298
Whole Dataset
0.7400 ±0.0010
This paper
334
Random
actual #334 vs paper #364 30 places worse
0.7040 ±0.0060
best reported
actual #334 vs paper #364 30 places worse
paper 0.6300 ±0.0120
paper 0.6300 ±0.0120 Δ at pub 0.0740
347
SimGC
0.6700 ±0.0070
This paper
351
MLP
0.6605 ±0.0020
360
SFGC
0.6440 ±0.0040
This paper
365
K-Center
0.6240 ±0.0050
This paper
375
SGDD
0.5930 ±0.0170
This paper
376
Herding
0.5910 ±0.0010
This paper
380
GCond
0.5640 ±0.0100
This paper
385
GCDM
0.5350 ±0.0110
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 Best today — OK at publication; today's leaderboard best is elsewhere