DRGCN [47] | 75.46  ±0.97 | 62.65  ±1.09 | 80.46  ±3.08 | 55.55  ±22.56 | 83.23  ±0.69 | — | 32.85  ±2.01 | 23.41  ±0.95 | 22.30  ±0.63
DPGNN [53] | 72.73  ±2.46 | 58.77  ±2.86 | 80.49  ±2.78 | 55.27  ±10.24 | 83.37  ±2.87 | — | 30.06  ±3.08 | 21.67  ±1.65 | 17.38  ±2.51
ImGAGN [39] | 78.60  ±0.61 | 61.70  ±0.54 | 81.96  ±0.12 | 66.70  ±1.20 | 83.79  ±0.37 | — | 26.45  ±2.53 | 18.76  ±1.74 | 21.55  ±0.86
GraphSMOTE [69] | 77.03  ±0.42 | 61.20  ±0.44 | 80.93  ±0.18 | 65.39  ±0.90 | 83.76  ±0.53 | — | 22.93  ±1.31 | 14.71  ±1.38 | 21.13  ±0.71
GraphENS [35] | 78.26  ±0.91 | 61.86  ±0.77 | 82.03  ±0.16 | 68.39  ±0.89 | 85.64  ±1.22 | 27.92  ±0.16 | 23.99  ±1.98 | 18.80  ±1.62 | 21.91  ±0.35
GraphMixup [56] | 77.54  ±0.73 | 66.34  ±0.98 | 82.92  ±0.10 | 70.81  ±0.92 | 86.84  ±0.40 | 26.14  ±0.38 | 33.76  ±0.38 | 23.78  ±0.26 | 22.25  ±0.97
LTE4G [63] | 78.45  ±1.10 | 64.35  ±2.04 | 83.19  ±0.32 | 62.28  ±3.47 | 84.09  ±4.41 | — | 34.00  ±0.67 | 23.45  ±0.31 | 22.75  ±1.17
TAM [48] | 79.34  ±0.61 | 61.95  ±0.33 | 74.23  ±0.77 | 68.53  ±0.72 | 85.48  ±1.39 | 27.93  ±0.22 | 25.40  ±1.86 | 18.43  ±2.12 | 22.10  ±0.54
TOPOAUC [8] | 81.95  ±0.36 | 69.28  ±0.45 | — | 57.76  ±1.85 | 79.31  ±2.25 | — | 35.85  ±0.79 | 23.70  ±0.44 | 24.43  ±0.69
GraphSHA [24] | 78.26  ±0.91 | 61.84  ±0.77 | 82.02  ±0.15 | 68.61  ±0.67 | 85.62  ±1.21 | 28.20  ±0.16 | 23.99  ±1.98 | 18.80  ±1.62 | 21.91  ±0.36
$\bm{\rho}=$ 20 (Low)
GCN (bb.) [21] | 71.15  ±0.30 | 43.71  ±0.54 | 45.71  ±0.16 | 39.11  ±0.43 | 48.99  ±8.51 | 33.94  ±0.26 | 16.67  ±0.52 | 9.83  ±0.49 | 12.18  ±0.67
DRGCN [47] | 64.43  ±1.52 | 47.50  ±1.46 | 53.83  ±4.78 | 41.55  ±2.42 | 74.51  ±8.46 | — | 17.22  ±0.44 | 11.01  ±0.88 | 16.43  ±0.57
DPGNN [53] | 68.70  ±3.61 | 50.06  ±2.10 | 81.54  ±2.42 | 66.97  ±8.96 | 79.53  ±8.70 | — | 26.03  ±1.83 | 21.53  ±2.14 | 18.48  ±1.50
ImGAGN [39] | 68.69  ±3.93 | 48.40  ±3.58 | 67.80  ±1.41 | 72.51  ±1.28 | 75.49  ±1.64 | — | 16.94  ±2.14 | 13.91  ±2.77 | 21.04  ±3.16
GraphSMOTE [69] | 72.71  ±0.31 | 45.21  ±0.95 | 45.35  ±0.21 | 49.30  ±4.76 | 79.64  ±0.98 | — | 18.72  ±0.26 | 8.36  ±0.36 | 16.26  ±0.84
GraphENS [35] | 77.16  ±0.50 | 57.80  ±0.96 | 79.71  ±0.24 | 77.89  ±0.69 | 88.20  ±0.28 | 30.16  ±0.37 | 19.58  ±0.99 | 16.73  ±1.73 | 23.30  ±0.38
GraphMixup [56] | 74.03  ±0.62 | 55.31  ±0.69 | 73.63  ±0.11 | 81.54  ±0.58 | 80.83  ±0.63 | 32.38  ±0.17 | 25.57  ±0.76 | 13.17  ±0.79 | 18.35  ±0.54
LTE4G [63] | 76.46  ±1.17 | 57.35  ±1.49 | 82.12  ±0.27 | 69.02  ±3.78 | 85.23  ±1.34 | — | 25.96  ±0.35 | 15.13  ±0.80 | 21.27  ±0.48
TAM [48] | 78.83  ±0.32 | 60.12  ±0.31 | 80.75  ±0.15 | 78.10  ±0.65 | 88.16  ±0.30 | 30.30  ±0.29 | 19.99  ±1.21 | 17.29  ±0.94 | 24.01  ±0.54
TOPOAUC [8] | 80.61  ±0.30 | 62.95  ±1.21 | — | 67.15  ±5.38 | 81.69  ±2.38 | — | 29.06  ±2.35 | 18.77  ±1.36 | 23.61  ±0.24
GraphSHA [24] | 77.66  ±0.46 | 55.76  ±0.85 | 76.17  ±0.37 | 75.43  ±0.47 | 89.04  ±0.27 | 32.09  ±0.23 | 19.64  ±1.26 | 16.73  ±1.73 | 20.36  ±0.97
$\bm{\rho}=$ 100 (High)
GCN (bb.) [21] | 43.97  ±7.75 | 30.77  ±0.21 | 34.08  ±0.77 | 20.44  ±1.45 | 16.99  ±0.64 | 31.11  ±0.50 | 14.79  ±0.11 | 8.27  ±0.17 | 9.01  ±0.66
DRGCN [47] | 47.47  ±4.00 | 34.83  ±2.80 | 36.44  ±4.29 | 33.60  ±1.15 | 52.58  ±6.68 | — | 15.02  ±0.26 | 8.83  ±1.09 | 12.38  ±1.05
DPGNN [53] | 58.66  ±3.44 | 41.53  ±3.59 | 75.47  ±3.04 | 68.30  ±8.53 | 84.82  ±1.94 | — | 23.96  ±2.16 | 18.85  ±2.36 | 19.62  ±1.15
ImGAGN [39] | 55.03  ±5.32 | 43.92  ±4.61 | 50.74  ±1.93 | 57.30  ±5.51 | 67.27  ±4.58 | — | 14.12  ±2.75 | 10.62  ±4.19 | 18.84  ±2.87
GraphSMOTE [69] | 58.93  ±0.54 | 35.40  ±0.93 | 34.78  ±0.80 | 17.90  ±1.20 | 16.34  ±0.04 | — | 15.13  ±0.16 | 9.31  ±0.29 | 9.05  ±0.76
GraphENS [35] | 74.91  ±0.66 | 56.58  ±0.60 | 74.36  ±0.40 | 78.75  ±0.59 | 88.53  ±0.25 | 30.89  ±0.38 | 20.80  ±0.64 | 17.96  ±1.89 | 18.47  ±2.45
GraphMixup [56] | 55.91  ±0.61 | 38.36  ±0.24 | 55.24  ±0.21 | 46.92  ±0.61 | 53.54  ±5.72 | 33.18  ±0.16 | 20.02  ±0.11 | 10.07  ±0.17 | 14.46  ±0.78
LTE4G [63] | 62.11  ±1.29 | 45.67  ±1.91 | 66.79  ±15.94 | 70.80  ±2.70 | 83.24  ±2.67 | — | 21.02  ±1.06 | 10.61  ±0.51 | 17.88  ±0.67
TAM [48] | 77.07  ±0.57 | 57.67  ±0.46 | 79.34  ±0.21 | 78.97  ±0.29 | 88.44  ±0.23 | 30.91  ±0.45 | 20.37  ±1.49 | 20.28  ±1.48 | 21.33  ±0.31
TOPOAUC [8] | 70.01  ±0.95 | 58.92  ±2.94 | — | — | 80.80  ±3.23 | — | 24.41  ±1.51 | 13.62  ±2.00 | 22.40  ±0.40
GraphSHA [24] | 75.86  ±0.58 | 51.99  ±0.68 | 64.66  ±1.02 | 72.46  ±1.10 | 88.36  ±0.43 | 27.92  ±0.33 | 19.96  ±1.82 | 17.87  ±1.99 | 18.05  ±2.33

Table D.4: AUC-ROC score (% ± standard deviation) of node classification on
manipulated class-imbalanced graph datasets with changing imbalance levels
over 10 runs. “—” denotes out of memory or time limit. The best results are
shown in bold and the runner-ups are underlined.

Algorithm |  Cora 0.81 |  CiteSeer 0.74 |  PubMed 0.80 |  Computers 0.78 |  Photo 0.82 |  ogbn-arXiv 0.65 |  Chameleon 0.23 |  Squirrel 0.22 |  Actor 0.22
---|---|---|---|---|---|---|---|---|---
$\bm{\rho}=$ 1 (Balanced)
GCN (bb.) [21] | 96.08  ±0.47 | 89.74  ±0.11 | 94.55  ±0.04 | 97.61  ±0.04 | 98.73  ±0.04 | 93.39  ±0.10 | 63.48  ±0.66 | 51.32  ±0.95 | 53.22  ±0.58
DRGCN [47] | 95.01  ±0.30 | 89.32  ±0.22 | 94.73  ±0.41 | 93.43  ±11.13 | 98.49  ±0.12 | — | 64.93  ±0.49 | 55.40  ±0.32 | 54.28  ±0.45
DPGNN [53] | 93.84  ±0.91 | 86.15  ±1.58 | 92.59  ±2.58 | 95.06  ±2.35 | 97.85  ±0.63 | — | 63.30  ±1.93 | 55.05  ±1.31 | 52.51  ±2.20
ImGAGN [39] | 96.49  ±0.17 | 89.97  ±0.13 | 94.52  ±0.03 | 97.12  ±0.13 | 98.53  ±0.08 | — | 64.90  ±0.86 | 51.28  ±0.53 | 53.66  ±1.05
GraphSMOTE [69] | 95.88  ±0.35 | 89.48  ±0.13 | 93.94  ±0.06 | 97.18  ±0.09 | 98.64  ±0.04 | — | 60.33  ±3.34 | 51.21  ±0.33 | 53.70  ±0.36
GraphENS [35] | 96.08  ±0.47 | 89.74  ±0.11 | 94.55  ±0.04 | 97.67  ±0.07 | 98.76  ±0.11 | 93.33  ±0.07 | 63.48  ±0.66 | 51.32  ±0.95 | 53.22  ±0.58
GraphMixup [56] | 96.42  ±0.25 | 89.83  ±0.94 | 95.16  ±0.04 | 97.96  ±0.13 | 98.79  ±0.03 | 92.64  ±0.09 | 63.16  ±0.65 | 54.01  ±0.31 | 53.82  ±0.76
LTE4G [63] | 96.54  ±0.39 | 89.00  ±0.67 | 95.61  ±0.05 | 95.88  ±3.08 | 98.17  ±0.56 | — | 65.42  ±0.49 | 55.22  ±0.40 | 57.75  ±0.64
TAM [48] | 96.85  ±0.04 | 89.77  ±0.08 | 92.62  ±0.12 | 97.69  ±0.06 | 98.71  ±0.16 | 93.34  ±0.06 | 60.11  ±1.56 | 51.67  ±0.78 | 51.84  ±0.46
TOPOAUC [8] | 97.56  ±0.04 | 91.89  ±0.23 | — | 91.26  ±2.37 | 94.11  ±1.46 | — | 67.70  ±0.88 | 55.43  ±0.09 | 57.17  ±0.53
GraphSHA [24] | 96.08  ±0.47 | 89.74  ±0.11 | 94.54  ±0.04 | 97.69  ±0.06 | 98.76  ±0.11 |  93.50  ±0.08 | 63.48  ±0.66 | 51.32  ±0.95 | 53.22  ±0.58
$\bm{\rho}=$ 20 (Low)
GCN (bb.) [21] | 95.04  ±0.08 | 86.57  ±0.19 | 92.23  ±0.09 | 94.41  ±0.53 | 94.35  ±0.96 | 93.54  ±0.09 | 57.70  ±0.42 | 51.70  ±0.08 | 52.05  ±0.36
DRGCN [47] | 92.68  ±0.30 | 84.92  ±0.63 | 92.04  ±0.35 | 93.84  ±0.50 | 98.22  ±0.49 | — | 56.19  ±0.66 | 49.42  ±0.68 | 55.20  ±0.28
DPGNN [53] | 92.41  ±1.08 | 81.04  ±1.44 | 93.24  ±1.77 | 95.03  ±1.93 | 96.30  ±2.20 | — | 60.45  ±2.11 | 55.66  ±1.56 | 51.20  ±0.71
ImGAGN [39] | 92.89  ±0.45 | 83.52  ±0.51 | 90.53  ±1.69 | 94.55  ±1.38 | 95.25  ±1.19 | — | 53.11  ±2.76 | 49.98  ±0.74 | 54.92  ±1.99
GraphSMOTE [69] | 95.14  ±0.16 | 86.59  ±0.27 | 91.77  ±0.09 | 96.51  ±0.41 | 98.28  ±0.31 | — | 56.92  ±0.23 | 51.71  ±0.06 | 53.79  ±0.27
GraphENS [35] | 96.32  ±0.13 | 87.46  ±0.43 | 93.26  ±0.11 | 97.70  ±0.09 | 98.71  ±0.05 | 93.04  ±0.08 | 58.54  ±2.61 | 52.33  ±0.77 | 56.10  ±0.13
GraphMixup [56] | 96.23  ±0.13 | 85.86  ±0.30 | 93.81  ±0.05 | 98.24  ±0.05 | 98.27  ±0.09 | 92.75  ±0.09 | 61.05  ±0.37 | 53.78  ±0.39 | 52.70  ±0.12
LTE4G [63] | 95.67  ±0.33 | 86.14  ±0.99 | 94.90  ±0.29 | 96.85  ±0.25 | 98.69  ±0.25 | — | 63.31  ±0.60 | 53.83  ±0.29 | 54.36  ±0.44
TAM [48] | 96.74  ±0.07 | 88.41  ±0.19 | 93.71  ±0.07 | 97.69  ±0.10 | 98.71  ±0.04 | 93.07  ±0.07 | 58.71  ±1.96 | 51.17  ±1.18 | 55.72  ±0.17
TOPOAUC [8] | 97.09  ±0.16 | 88.62  ±0.59 | — | 91.04  ±1.72 | 93.96  ±1.62 | — | 65.86  ±0.82 | 53.47  ±0.49 | 54.78  ±0.25
GraphSHA [24] | 96.27  ±0.05 | 87.36  ±0.22 | 93.14  ±0.10 | 97.78  ±0.06 | 98.74  ±0.06 | 93.39  ±0.11 | 58.19  ±2.52 | 52.33  ±0.77 | 52.48  ±1.05
$\bm{\rho}=$ 100 (High)
GCN (bb.) [21] | 91.55  ±0.80 | 80.26  ±0.32 | 79.13  ±1.41 | 87.24  ±1.56 | 76.98  ±1.42 |  92.87  ±0.12 | 57.86  ±0.65 | 51.16  ±0.06 | 50.79  ±0.79
DRGCN [47] | 89.80  ±0.54 | 79.58  ±1.24 | 84.19  ±2.66 | 92.09  ±0.75 | 96.50  ±0.63 | — | 55.79  ±1.06 | 49.24  ±0.39 | 54.87  ±0.25
DPGNN [53] | 87.41  ±2.09 | 78.59  ±1.51 | 90.02  ±2.99 | 95.34  ±1.58 | 97.09  ±0.57 | — | 59.14  ±2.36 | 54.25  ±1.11 | 50.35  ±0.72
ImGAGN [39] | 88.38  ±1.39 | 81.37  ±0.69 | 87.52  ±1.15 | 92.75  ±1.38 | 94.82  ±0.72 | — | 52.73  ±2.84 | 49.44  ±0.71 | 53.60  ±1.51
GraphSMOTE [69] | 93.29  ±0.14 | 82.56  ±0.37 | 78.88  ±1.27 | 89.52  ±1.39 | 84.03  ±1.44 | — | 56.82  ±0.53 | 51.49  ±0.11 | 52.51  ±2.31
GraphENS [35] | 95.55  ±0.13 | 85.91  ±0.32 | 91.38  ±0.14 |  97.74 ±0.06 | 98.65  ±0.03 | 92.83  ±0.09 | 58.15  ±1.92 | 52.87  ±0.55 | 50.91  ±1.27
GraphMixup [56] | 92.31  ±0.22 | 82.50  ±0.12 | 90.58  ±0.09 | 97.06  ±0.17 | 93.85  ±0.69 | 92.03  ±0.09 | 58.73  ±0.27 | 53.24  ±0.08 | 52.46  ±0.14
LTE4G [63] | 92.82  ±0.56 | 83.87  ±1.13 | 90.77  ±2.91 | 97.19  ±0.19 | 97.26  ±0.46 | — | 59.10  ±0.89 | 52.60  ±0.18 | 53.96  ±0.67
TAM [48] | 96.24  ±0.04 | 87.22  ±0.25 | 93.14  ±0.05 | 97.75  ±0.05 | 98.65  ±0.03 | 92.84  ±0.10 | 56.81  ±2.37 | 52.99  ±0.46 | 52.42  ±0.14
TOPOAUC [8] | 90.42  ±1.64 | 86.50  ±0.50 | — | — | 93.14  ±0.96 | — | 61.71  ±0.80 | 52.17  ±0.28 | 53.31  ±0.34
GraphSHA [24] | 95.73  ±0.11 | 85.10  ±0.16 | 90.09  ±3.59 | 97.51  ±0.14 | 98.62  ±0.06 | 92.18  ±0.13 | 56.00  ±2.91 | 52.87  ±0.55 | 50.72  ±0.98

#####  D.1.2 Performance of Node-Level Local Topology-Imbalanced Algorithms

Table D.5: Accuracy score (% ± standard deviation) of node classification on
manipulated local topology-imbalanced graph datasets with changing imbalance
levels over 10 runs. “—” denotes out of memory or time limit. The best results
are shown in bold and the runner-ups are underlined.

Algorithm |  Cora 0.81 |  CiteSeer 0.74 |  PubMed 0.80 |  Computers 0.78 |  Photo 0.82 |  ogbn-arXiv 0.65 |  Chameleon 0.23 |  Squirrel 0.22 |  Actor 0.22
---|---|---|---|---|---|---|---|---|---
Imbalance Ratio: Low
GCN (bb.) [21] | 80.16  ±0.97 | 66.99  ±1.78 | 83.97  ±0.14 | 70.39  ±1.68 | 87.28  ±2.77 | 55.45  ±0.06 | 50.42  ±1.22 | 30.87  ±0.60 | 24.23  ±1.74
DEMO-Net [55] | 81.40  ±0.43 | 68.42  ±0.72 | 82.70  ±0.51 | 79.07  ±0.53 | 88.06  ±1.81 | 65.31  ±0.15 | 56.18  ±0.62 | 38.86  ±0.78 | 29.34  ±0.59
meta-tail2vec [30] | 38.11  ±1.36 | 24.77  ±2.39 | 59.93  ±1.95 | 71.13  ±0.41 | 77.16  ±0.33 | 33.61  ±0.25 | 41.45  ±0.46 | 24.47  ±0.18 | 25.98  ±0.07
Tail-GNN [29] | 80.16  ±0.64 | 70.37  ±0.57 | 84.56  ±0.30 | 86.40  ±0.92 | 92.79  ±0.19 | — | 51.87  ±0.79 | 31.89  ±0.93 | 28.67  ±0.47
Cold Brew [70] | 75.37  ±1.07 | 65.16  ±0.59 | 86.11  ±0.05 | 79.61  ±0.40 | 85.94  ±0.23 | 68.50  ±0.07 | 58.78  ±0.19 | 39.57  ±0.19 | 32.93  ±0.45
LTE4G [63] | 82.10  ±0.56 | 69.17  ±0.96 | 84.64  ±0.30 | 81.24  ±2.79 | 92.47  ±0.21 | — | 58.61  ±0.98 | 25.74  ±2.58 | 24.53  ±1.12
RawlsGCN [19] | 79.95  ±0.29 | 72.20  ±0.39 | 85.97  ±0.12 | 78.74  ±2.01 | 87.89  ±0.10 | 41.70  ±0.23 | 44.91  ±1.15 | 29.68  ±0.83 | 28.54  ±0.12
GraphPatcher [17] | 84.00  ±0.62 | 72.34  ±0.32 | 85.58  ±0.13 | 87.60  ±0.23 | 93.20  ±0.32 | 66.35  ±0.09 | 55.77  ±1.04 | 35.16  ±0.22 | 27.15  ±0.80
Imbalance Ratio: Mid
GCN (bb.) [21] | 80.16  ±1.09 | 66.87  ±0.85 | 83.97  ±0.13 | 71.65  ±2.10 | 89.43  ±0.58 | 52.93  ±0.33 | 52.74  ±0.60 | 28.70  ±0.68 | 21.55  ±1.74
DEMO-Net [55] | 80.37  ±0.52 | 69.73  ±1.31 | 84.11  ±0.20 | 79.38  ±0.98 | 88.09  ±1.30 | 65.81  ±0.11 | 55.51  ±0.87 | 39.45  ±0.62 | 29.12  ±0.30
meta-tail2vec [30] | 32.17  ±0.68 | 29.97  ±3.61 | 59.82  ±2.86 | 68.17  ±1.07 | 79.82  ±1.02 | 33.71  ±1.16 | 38.78  ±0.44 | 24.90  ±0.25 | 26.09  ±0.07
Tail-GNN [29] | 79.05  ±1.15 | 69.97  ±1.03 | 85.78  ±0.41 | 84.09  ±1.01 | 92.21  ±0.09 | — | 53.20  ±0.80 | 30.43  ±1.06 | 28.02  ±0.71
Cold Brew [70] | 73.84  ±2.10 | 67.42  ±0.97 | 86.51  ±0.04 | 80.19  ±0.24 | 88.13  ±0.24 |  69.97  ±0.07 | 59.16  ±0.40 | 43.04  ±0.24 | 33.01  ±0.19
LTE4G [63] | 82.54  ±0.46 | 70.55  ±0.54 | 84.77  ±0.78 | 81.32  ±2.21 | 91.09  ±0.19 | — | 55.84  ±2.86 | 32.43  ±3.31 | 24.00  ±0.49
RawlsGCN [19] | 80.52  ±0.14 | 72.38  ±0.43 | 86.05  ±0.12 | 78.78  ±1.40 | 90.53  ±1.32 | 40.00  ±0.05 | 44.96  ±0.79 | 29.93  ±0.65 | 28.29  ±0.24
GraphPatcher [17] | 83.25  ±0.42 | 73.38  ±0.42 | 85.60  ±0.16 | 83.68  ±0.69 | 92.28  ±0.06 | 66.74  ±0.04 | 55.19  ±0.41 | 36.94  ±0.11 | 23.85  ±0.92
Imbalance Ratio: High
GCN (bb.) [21] | 78.70  ±1.05 | 65.07  ±0.81 | 83.87  ±0.32 | 68.15  ±4.13 | 89.42  ±1.24 | 50.72  ±0.30 | 53.33  ±1.09 | 29.56  ±2.72 | 23.86  ±0.90
DEMO-Net [55] | 78.23  ±1.32 | 67.11  ±0.44 | 83.51  ±0.29 | 78.34  ±0.88 | 88.08  ±0.30 | 65.76  ±0.18 | 54.08  ±1.41 | 36.98  ±1.27 | 28.96  ±0.30
meta-tail2vec [30] | 38.16  ±1.42 | 21.62  ±1.70 | 58.39  ±2.25 | 71.03  ±2.20 | 66.37  ±2.96 | 35.31  ±0.21 | 37.94  ±0.52 | 25.18  ±0.30 | 25.98  ±0.03
Tail-GNN [29] | 81.20  ±0.55 | 69.69  ±0.55 | 84.95  ±0.37 | 86.39  ±0.82 | 92.55  ±0.40 | — | 53.00  ±0.89 | 31.08  ±0.91 | 28.36  ±1.16
Cold Brew [70] | 75.44  ±2.31 | 66.12  ±0.71 | 86.44  ±0.02 | 78.59  ±0.10 | 86.83  ±0.27 | 70.32  ±0.08 | 59.47  ±0.14 | 40.16  ±0.16 | 33.44  ±0.22
LTE4G [63] | 81.93  ±1.43 | 67.09  ±0.73 | 84.30  ±0.49 | 83.33  ±1.59 | 92.12  ±0.32 | — | 56.39  ±2.69 | 30.16  ±4.09 | 23.83  ±0.85
RawlsGCN [19] | 81.66  ±0.17 | 69.88  ±0.74 | 85.72  ±0.07 | 79.27  ±0.41 | 87.99  ±1.16 | 39.14  ±0.16 | 42.22  ±0.37 | 28.54  ±0.79 | 29.30  ±0.17
GraphPatcher [17] | 80.77  ±0.23 | 73.13  ±0.48 | 85.74  ±0.14 | 85.47  ±0.16 | 93.57  ±0.13 | 67.38  ±0.06 | 56.74  ±0.25 | 37.12  ±0.18 | 25.48  ±0.49

Table D.6: Balanced Accuracy score (% ± standard deviation) of node
classification on manipulated local topology-imbalanced graph datasets with
changing imbalance levels over 10 runs. “—” denotes out of memory or time
limit. Best results are shown in bold and the runner-ups are underlined.

Algorithm |  Cora 0.81 |  CiteSeer 0.74 |  PubMed 0.80 |  Computers 0.78 |  Photo 0.82 |  ogbn-arXiv 0.65 |  Chameleon 0.23 |  Squirrel 0.22 |  Actor 0.22
---|---|---|---|---|---|---|---|---|---
Imbalance Ratio: Low
GCN (bb.) [21] | 81.19  ±0.89 | 63.72  ±2.11 | 84.31  ±0.14 | 77.82  ±1.32 | 86.91  ±2.30 | 22.36  ±0.15 | 50.82  ±0.89 | 30.86  ±0.60 | 23.02  ±1.14
DEMO-Net [55] | 82.53  ±0.35 | 65.58  ±0.71 | 83.84  ±0.08 | 84.87  ±0.25 | 90.06  ±0.82 | 41.57  ±1.20 | 56.18  ±0.45 | 38.85  ±0.78 | 26.59  ±0.61
meta-tail2vec [30] | 27.64  ±1.24 | 19.99  ±1.80 | 53.78  ±1.75 | 55.68  ±4.36 | 80.39  ±0.35 | 7.46  ±0.43 | 40.58  ±0.42 | 24.46  ±0.16 | 20.12  ±0.15
Tail-GNN [29] | 82.10  ±0.28 | 66.78  ±0.30 | 85.42  ±0.41 | 90.80  ±0.53 | 93.57  ±0.77 | — | 51.96  ±0.99 | 31.89  ±0.93 | 28.28  ±0.30
Cold Brew [70] | 77.41  ±0.62 | 62.25  ±1.02 | 86.11  ±0.05 | 85.58  ±0.35 | 88.67  ±0.18 | 47.29  ±0.12 | 58.05  ±0.20 | 39.56  ±0.19 | 29.01  ±1.40
LTE4G [63] | 82.68  ±0.43 | 67.45  ±0.40 | 85.15  ±0.25 | 87.35  ±2.33 | 92.86  ±0.44 | — | 58.15  ±0.91 | 25.73  ±2.58 | 24.31  ±0.62
RawlsGCN [19] | 81.80  ±0.21 | 68.80  ±0.27 | 86.76  ±0.13 | 84.67  ±0.64 | 90.59  ±0.31 | 13.32  ±0.08 | 45.15  ±0.83 | 29.69  ±0.83 | 28.13  ±0.12
GraphPatcher [17] | 84.66  ±0.47 | 68.56  ±0.16 | 85.68  ±0.19 | 90.73  ±0.18 | 93.61  ±0.26 | 43.97  ±0.09 | 55.28  ±1.02 | 35.15  ±0.22 | 22.46  ±0.46
Imbalance Ratio: Mid
GCN (bb.) [21] | 81.54  ±0.39 | 63.00  ±0.81 | 84.46  ±0.13 | 78.91  ±2.60 | 89.02  ±0.58 | 18.12  ±0.38 | 51.74  ±0.65 | 28.69  ±0.68 | 21.25  ±0.33
DEMO-Net [55] | 81.75  ±0.26 | 65.52  ±1.00 | 84.99  ±0.08 | 86.24  ±0.63 | 89.43  ±0.90 | 42.88  ±0.66 | 55.37  ±1.14 | 39.45  ±0.62 | 26.70  ±0.17
meta-tail2vec [30] | 32.56  ±0.98 | 25.17  ±1.60 | 56.16  ±1.92 | 55.60  ±4.13 | 81.26  ±1.78 | 7.46  ±0.68 | 39.92  ±0.52 | 24.91  ±0.25 | 20.08  ±0.07
Tail-GNN [29] | 81.47  ±0.27 | 66.05  ±0.65 | 86.64  ±0.30 | 90.06  ±0.28 | 93.08  ±0.19 | — | 53.40  ±0.71 | 30.44  ±1.05 | 26.26  ±0.73
Cold Brew [70] | 76.00  ±1.85 | 62.88  ±1.10 | 86.41  ±0.26 | 85.62  ±0.07 | 89.20  ±1.85 | 47.73  ±0.13 | 58.71  ±0.46 | 43.04  ±0.25 | 30.65  ±0.19
LTE4G [63] | 82.79  ±0.32 | 65.79  ±0.52 | 85.07  ±0.67 | 87.16  ±1.99 | 92.38  ±0.17 | — | 55.04  ±2.99 | 32.43  ±3.32 | 24.14  ±0.56
RawlsGCN [19] | 82.11  ±0.18 | 67.74  ±0.26 | 86.89  ±0.16 | 84.76  ±1.49 | 91.50  ±0.20 | 11.62  ±0.13 | 44.42  ±1.19 | 29.93  ±0.65 | 27.29  ±0.20
GraphPatcher [17] | 83.94  ±0.20 | 69.17  ±0.22 | 85.72  ±0.08 | 90.95  ±0.21 | 93.21  ±0.06 | 38.49  ±0.41 | 54.39  ±0.41 | 36.93  ±0.11 | 23.10  ±0.54
Imbalance Ratio: High
GCN (bb.) [21] | 81.68  ±0.84 | 62.76  ±0.69 | 84.70  ±0.07 | 78.15  ±3.40 | 90.19  ±0.35 | 15.93  ±0.27 | 52.93  ±1.49 | 29.54  ±2.72 | 22.83  ±0.57
DEMO-Net [55] | 82.14  ±0.32 | 64.16  ±0.76 | 84.70  ±0.09 | 87.19  ±0.50 | 90.51  ±0.10 | 42.00  ±1.23 | 54.11  ±1.30 | 36.37  ±1.66 | 27.16  ±0.28
meta-tail2vec [30] | 25.23  ±4.75 | 17.49  ±1.12 | 52.61  ±2.40 | 67.44  ±2.57 | 72.79  ±8.67 | 7.82  ±0.12 | 36.66  ±0.63 | 25.20  ±0.30 | 20.03  ±0.03
Tail-GNN [29] | 83.79  ±0.49 | 67.15  ±0.12 | 86.07  ±0.12 | 90.72  ±0.50 | 94.62  ±0.22 | — | 53.12  ±0.69 | 31.09  ±0.91 | 27.36  ±0.70
Cold Brew [70] | 78.25  ±1.72 | 63.45  ±1.10 | 86.43  ±0.09 | 85.73  ±0.10 | 90.14  ±0.65 | 48.43  ±0.16 | 59.66  ±0.17 | 40.16  ±0.16 | 30.68  ±0.18
LTE4G [63] | 84.15  ±1.36 | 64.63  ±0.65 | 85.12  ±0.38 | 89.78  ±0.59 | 94.24  ±0.28 | — | 56.25  ±3.03 | 30.15  ±4.10 | 24.03  ±0.53
RawlsGCN [19] | 83.19  ±0.24 | 67.51  ±0.41 | 86.60  ±0.10 | 86.25  ±0.13 | 91.82  ±0.24 | 10.65  ±0.07 | 42.87  ±0.81 | 28.54  ±0.79 | 28.14  ±0.20
GraphPatcher [17] | 83.91  ±0.11 | 68.89  ±0.09 | 85.78  ±0.18 | 91.23  ±0.05 | 93.57  ±0.13 | 40.59  ±0.39 | 56.78  ±0.25 | 37.11  ±0.18 | 23.98  ±0.22

Table D.7: Macro-F1 score (% ± standard deviation) of node classification on
manipulated local topology-imbalanced graph datasets with changing imbalance
levels over 10 runs. “—” denotes out of memory or time limit. The best results
are shown in bold and the runner-ups are underlined.

Algorithm |  Cora 0.81 |  CiteSeer 0.74 |  PubMed 0.80 |  Computers 0.78 |  Photo 0.82 |  ogbn-arXiv 0.65 |  Chameleon 0.23 |  Squirrel 0.22 |  Actor 0.22
---|---|---|---|---|---|---|---|---|---
Imbalance Ratio: Low
GCN (bb.) [21] | 77.96  ±1.22 | 63.07  ±1.72 | 82.88  ±0.12 | 58.70  ±2.09 | 82.92  ±2.33 | 21.64  ±0.37 | 50.63  ±1.22 | 29.19  ±1.40 | 19.05  ±2.75
DEMO-Net [55] | 79.01  ±0.52 | 64.74  ±0.77 | 81.93  ±0.52 | 65.66  ±1.07 | 84.73  ±1.70 | 43.08  ±1.01 | 55.67  ±0.53 | 38.58  ±0.69 | 26.45  ±0.72
meta-tail2vec [30] | 23.87  ±1.96 | 11.60  ±2.38 | 53.82  ±1.49 | 50.14  ±3.23 | 71.66  ±0.31 | 6.68  ±0.82 | 40.11  ±0.47 | 22.06  ±1.32 | 9.48  ±1.49
Tail-GNN [29] | 77.91  ±0.37 | 66.32  ±0.45 | 84.05  ±0.30 | 75.59  ±0.45 | 89.56  ±0.35 | — | 51.09  ±0.80 | 29.90  ±0.46 | 26.95  ±0.65
Cold Brew [70] | 73.42  ±0.83 | 61.70  ±0.77 | 85.41  ±0.04 | 65.71  ±0.27 | 81.89  ±0.28 | 48.39  ±0.13 | 58.50  ±0.23 | 38.90  ±0.47 | 26.89  ±1.99
LTE4G [63] | 79.49  ±0.55 | 66.21  ±0.66 | 83.64  ±0.33 | 69.51  ±3.48 | 89.78  ±0.28 | — | 58.48  ±0.89 | 24.48  ±3.27 | 23.15  ±0.67
RawlsGCN [19] | 77.88  ±0.28 | 68.20  ±0.29 | 85.43  ±0.12 | 67.01  ±2.37 | 85.49  ±0.34 | 14.56  ±0.05 | 43.80  ±1.19 | 29.24  ±0.50 | 26.80  ±0.10
GraphPatcher [17] | 81.64  ±0.78 | 68.28  ±0.22 | 84.65  ±0.18 | 78.27  ±0.69 | 90.48  ±0.46 | 44.74  ±0.04 | 55.67  ±0.98 | 35.11  ±0.30 | 19.03  ±0.95
Imbalance Ratio: Mid
GCN (bb.) [21] | 78.43  ±0.94 | 62.70  ±0.77 | 82.81  ±0.10 | 60.43  ±2.57 | 84.99  ±0.76 | 17.40  ±0.42 | 52.11  ±0.66 | 27.48  ±1.74 | 19.37  ±1.28
DEMO-Net [55] | 78.11  ±0.54 | 65.23  ±1.02 | 83.44  ±0.20 | 67.75  ±0.73 | 84.14  ±1.52 | 44.63  ±0.59 | 55.17  ±0.98 | 38.93  ±0.60 | 26.48  ±0.39
meta-tail2vec [30] | 30.58  ±1.61 | 19.16  ±3.28 | 54.86  ±0.66 | 49.59  ±1.24 | 76.33  ±0.82 | 6.62  ±0.98 | 38.29  ±0.62 | 24.30  ±0.24 | 8.70  ±0.42
Tail-GNN [29] | 77.40  ±1.05 | 65.77  ±0.81 | 85.23  ±0.41 | 73.31  ±1.40 | 88.73  ±0.13 | — | 52.53  ±0.74 | 27.98  ±0.79 | 25.68  ±0.61
Cold Brew [70] | 71.85  ±2.17 | 62.70  ±1.00 | 85.69  ±0.07 | 66.03  ±0.20 | 84.26  ±0.16 | 49.82  ±0.18 | 58.91  ±0.46 | 42.07  ±0.40 | 30.71  ±0.20
LTE4G [63] | 80.29  ±0.45 | 65.76  ±0.47 | 83.66  ±0.88 | 68.65  ±3.35 | 87.57  ±0.13 | — | 55.32  ±2.93 | 32.20  ±3.71 | 22.78  ±0.50
RawlsGCN [19] | 78.30  ±0.26 | 67.50  ±0.18 | 85.49  ±0.14 | 66.62  ±2.07 | 87.77  ±1.45 | 12.56  ±0.20 | 44.44  ±1.11 | 29.48  ±0.49 | 26.32  ±0.21
GraphPatcher [17] | 80.92  ±0.42 | 68.95  ±0.25 | 84.65  ±0.18 | 74.74  ±0.73 | 88.89  ±0.11 | 40.76  ±0.32 | 54.72  ±0.35 | 37.06  ±0.11 | 22.28  ±0.58
Imbalance Ratio: High
GCN (bb.) [21] | 77.03  ±1.19 | 61.89  ±0.66 | 82.72  ±0.32 | 58.78  ±4.61 | 85.73  ±0.84 | 14.52  ±0.27 | 52.56  ±1.25 | 27.43  ±2.85 | 20.48  ±2.59
DEMO-Net [55] | 76.85  ±1.11 | 63.38  ±0.68 | 82.87  ±0.32 | 65.92  ±0.62 | 84.70  ±0.23 | 43.74  ±1.02 | 53.73  ±1.15 | 35.94  ±1.44 | 27.24  ±0.28
meta-tail2vec [30] | 21.82  ±5.45 | 7.56  ±2.36 | 52.03  ±3.18 | 54.07  ±2.19 | 65.22  ±7.60 | 6.71  ±0.18 | 34.06  ±1.22 | 23.00  ±0.60 | 8.30  ±0.06
Tail-GNN [29] | 79.66  ±0.57 | 66.29  ±0.33 | 84.31  ±0.35 | 75.04  ±1.16 | 89.67  ±0.39 | — | 52.67  ±0.68 | 28.08  ±1.18 | 25.85  ±0.75
Cold Brew [70] | 73.71  ±2.07 | 62.71  ±0.76 | 85.72  ±0.02 | 65.83  ±0.13 | 83.37  ±0.18 | 50.43  ±0.24 | 59.18  ±0.23 | 39.43  ±0.41 | 30.32  ±0.28
LTE4G [63] | 80.57  ±1.66 | 63.70  ±0.66 | 83.11  ±0.54 | 73.38  ±1.69 | 89.18  ±0.52 | — | 55.92  ±2.90 | 28.30  ±5.09 | 22.95  ±0.61
RawlsGCN [19] | 80.19  ±0.20 | 66.41  ±0.56 | 85.11  ±0.08 | 69.00  ±0.95 | 85.79  ±1.10 | 11.24  ±0.09 | 41.86  ±0.35 | 27.86  ±0.60 | 27.41  ±0.16
GraphPatcher [17] | 79.35  ±0.18 | 68.69  ±0.20 | 84.74  ±0.16 | 77.10  ±0.43 | 90.94  ±0.18 | 42.93  ±0.29 | 56.05  ±0.29 | 37.34  ±0.19 | 23.10  ±0.41

Table D.8: AUC-ROC score (% ± standard deviation) of node classification on
manipulated local topology-imbalanced graph datasets with changing imbalance
levels over 10 runs. “—” denotes out of memory or time limit. The best results
are shown in bold and the runner-ups are underlined.

Algorithm |  Cora 0.81 |  CiteSeer 0.74 |  PubMed 0.80 |  Computers 0.78 |  Photo 0.82 |  ogbn-arXiv 0.65 |  Chameleon 0.23 |  Squirrel 0.22 |  Actor 0.22
---|---|---|---|---|---|---|---|---|---
Imbalance Ratio: Low
GCN (bb.) [21] | 96.34  ±0.51 | 87.80  ±1.39 | 94.89  ±0.06 | 95.61  ±0.21 | 97.82  ±0.80 | 87.84  ±0.06 | 78.76  ±0.27 | 62.68  ±0.27 | 53.43  ±1.42
DEMO-Net [55] | 96.27  ±0.13 | 88.66  ±0.30 | 94.22  ±0.07 | 96.52  ±0.10 | 98.04  ±0.29 | 92.89  ±0.32 | 80.31  ±0.74 | 68.00  ±0.69 | 58.96  ±0.35
meta-tail2vec [30] | 62.83  ±1.22 | 53.44  ±2.06 | 71.50  ±3.86 | 89.26  ±0.64 | 94.95  ±0.16 | 62.42  ±2.26 | 69.63  ±0.28 | 53.44  ±0.62 | 50.50  ±0.35
Tail-GNN [29] | 96.55  ±0.06 | 89.11  ±0.56 | 94.28  ±0.69 | 97.92  ±0.11 | 98.70  ±0.13 | — | 76.76  ±0.44 | 63.91  ±1.16 | 59.72  ±0.56
Cold Brew [70] | 93.87  ±0.50 | 87.38  ±0.98 | 95.67  ±0.03 | 97.88  ±0.05 | 98.71  ±0.02 | 95.13  ±0.10 | 78.37  ±0.48 | 66.72  ±0.10 | 65.12  ±1.03
LTE4G [63] | 96.14  ±0.37 | 88.78  ±1.05 | 94.52  ±0.45 | 92.94  ±2.66 | 98.83  ±0.05 | — | 78.00  ±1.53 | 58.28  ±2.12 | 56.17  ±0.86
RawlsGCN [19] | 96.84  ±0.07 | 91.06  ±0.45 | 96.34  ±0.03 | 97.47  ±0.09 | 98.99  ±0.02 | 79.78  ±0.12 | 71.94  ±0.09 | 58.89  ±0.13 | 59.34  ±0.16
GraphPatcher [17] | 97.10  ±0.04 | 90.75  ±0.15 | 94.98  ±0.03 | 97.88  ±0.05 | 98.54  ±0.05 | 90.90  ±0.03 | 79.09  ±0.10 | 66.65  ±0.30 | 53.80  ±0.56
Imbalance Ratio: Mid
GCN (bb.) [21] | 95.88  ±0.29 | 87.55  ±0.33 | 95.07  ±0.06 | 95.70  ±0.77 | 98.05  ±0.11 | 86.55  ±0.29 | 78.60  ±0.38 | 62.45  ±0.74 | 51.23  ±0.46
DEMO-Net [55] | 95.59  ±0.08 | 88.31  ±0.26 | 94.78  ±0.05 | 97.14  ±0.18 | 97.75  ±0.13 | 93.29  ±0.35 | 80.31  ±0.91 | 67.96  ±0.32 | 59.54  ±0.45
meta-tail2vec [30] | 65.88  ±0.99 | 59.39  ±0.47 | 73.30  ±1.00 | 90.45  ±0.24 | 94.66  ±0.64 | 64.91  ±1.30 | 68.34  ±0.42 | 53.85  ±0.04 | 49.40  ±0.20
Tail-GNN [29] | 96.19  ±0.22 | 89.73  ±0.39 | 95.17  ±0.55 | 97.98  ±0.19 | 98.39  ±0.27 | — | 76.40  ±0.64 | 62.60  ±1.37 | 58.11  ±0.61
Cold Brew [70] | 93.14  ±0.87 | 88.06  ±1.14 | 96.06  ±0.05 | 98.03  ±0.02 | 98.40  ±0.33 | 95.66  ±0.06 | 77.61  ±0.13 | 68.96  ±0.16 | 65.47  ±0.17
LTE4G [63] | 95.16  ±0.59 | 89.69  ±0.44 | 94.41  ±0.96 | 93.05  ±2.75 | 97.74  ±0.33 | — | 77.80  ±1.83 | 61.90  ±1.44 | 55.08  ±0.68
RawlsGCN [19] | 96.65  ±0.07 | 91.53  ±0.43 | 96.29  ±0.04 | 97.53  ±0.07 | 98.97  ±0.02 | 79.84  ±0.22 | 71.42  ±0.15 | 59.10  ±0.08 | 59.19  ±0.14
GraphPatcher [17] | 96.66  ±0.08 | 91.74  ±0.09 | 94.63  ±0.02 | 98.05  ±0.07 | 98.14  ±0.02 | 92.04  ±0.11 | 78.36  ±0.26 | 66.40  ±0.12 | 54.64  ±0.62
Imbalance Ratio: High
GCN (bb.) [21] | 96.12  ±0.31 | 87.93  ±0.88 | 94.96  ±0.08 | 95.42  ±0.99 | 87.28  ±2.77 | 85.44  ±0.40 | 78.63  ±0.38 | 63.00  ±1.36 | 53.72  ±0.70
DEMO-Net [55] | 95.40  ±0.19 | 87.64  ±0.09 | 94.31  ±0.08 | 97.10  ±0.25 | 98.34  ±0.15 | 93.45  ±0.78 | 79.19  ±0.89 | 66.28  ±1.10 | 58.89  ±0.28
meta-tail2vec [30] | 61.19  ±1.02 | 49.89  ±1.49 | 69.63  ±3.44 | 92.90  ±0.31 | 91.77  ±2.16 | 62.67  ±1.41 | 68.62  ±0.77 | 55.24  ±0.23 | 50.04  ±0.34
Tail-GNN [29] | 96.80  ±0.05 | 89.96  ±0.42 | 95.10  ±0.15 | 97.93  ±0.10 | 98.60  ±0.13 | — | 76.81  ±0.31 | 64.39  ±0.42 | 59.60  ±1.06
Cold Brew [70] | 94.04  ±0.64 | 88.26  ±0.37 | 95.90  ±0.03 | 97.82  ±0.05 | 98.87  ±0.10 | 95.86  ±0.06 | 78.97  ±0.34 | 67.72  ±0.11 | 65.52  ±0.16
LTE4G [63] | 96.17  ±0.35 | 86.40  ±2.05 | 94.46  ±0.31 | 95.97  ±1.48 | 98.72  ±0.06 | — | 77.34  ±1.75 | 60.35  ±2.63 | 54.98  ±0.84
RawlsGCN [19] | 96.87  ±0.03 | 90.42  ±0.13 | 96.16  ±0.03 | 97.51  ±0.04 | 99.21  ±0.02 | 79.47  ±0.15 | 71.04  ±0.11 | 58.32  ±0.12 | 59.38  ±0.13
GraphPatcher [17] | 96.15  ±0.05 | 91.55  ±0.48 | 94.90  ±0.02 | 97.59  ±0.05 | 98.75  ±0.02 | 92.53  ±0.05 | 78.67  ±0.15 | 65.82  ±0.40 | 56.03  ±0.19

#####  D.1.3 Performance of Node-Level Global Topology-Imbalanced Algorithms

Table D.9: Accuracy score (% ± standard deviation) of node classification on
manipulated global topology-imbalanced graph datasets with changing imbalance
levels over 10 runs. “—” denotes out of memory or time limit. The best results
are shown in bold and the runner-ups are underlined.

Algorithm |  Cora 0.81 |  CiteSeer 0.74 |  PubMed 0.80 |  Computers 0.78 |  Photo 0.82 |  ogbn-arXiv 0.65 |  Chameleon 0.23 |  Squirrel 0.22 |  Actor 0.22
---|---|---|---|---|---|---|---|---|---
Imbalance Ratio: Low
GCN (bb.) [21] | 81.09  ±0.76 | 70.39  ±1.11 | 84.44  ±0.20 | 76.23  ±2.16 | 88.16  ±1.86 | 53.09  ±0.17 | 37.80  ±0.59 | 25.15  ±0.57 | 24.34  ±0.78
ReNode [7] | 81.94  ±0.48 | 71.93  ±0.88 | 83.86  ±0.13 | 79.42  ±1.70 | 89.91  ±0.51 | 52.75  ±0.14 | 37.67  ±0.49 | 25.36  ±0.49 | 24.65  ±0.28
TAM [48] | 81.48  ±0.30 | 74.06  ±0.12 | 84.26  ±0.08 | 84.17  ±0.18 | 91.93  ±0.22 | 54.16  ±0.05 | 38.78  ±0.17 | 25.64  ±0.12 | 24.77  ±0.33
PASTEL [49] | 82.49  ±0.34 | 74.38  ±0.31 | — | 85.08  ±0.84 | 91.22  ±0.40 | — | 54.05  ±1.13 | 34.01  ±0.57 | 29.50  ±0.39
TOPOAUC [8] | 81.38  ±0.80 | 72.31  ±0.75 | — | 77.23  ±1.31 | 89.04  ±0.96 | — | 37.68  ±0.81 | 23.52  ±0.78 | 25.88  ±0.97
HyperIMBA [12] | 80.67  ±0.64 | 73.46  ±0.70 | 85.19  ±0.26 | 85.22  ±0.64 | 92.75  ±0.13 | — | 43.48  ±1.30 | 32.69  ±0.66 | 27.09  ±3.15
Imbalance Ratio: High
GCN (bb.) [21] | 79.10  ±1.28 | 68.37  ±1.73 | 83.44  ±0.16 | 75.02  ±2.20 | 86.32  ±1.90 | 51.04  ±0.18 | 33.90  ±0.70 | 23.27  ±0.82 | 22.40  ±0.68
ReNode [7] | 79.91  ±1.52 | 69.89  ±0.73 | 82.97  ±0.12 | 77.95  ±1.71 | 87.80  ±0.52 | 50.68  ±0.15 | 32.92  ±0.98 | 23.80  ±0.59 | 22.39  ±0.62
TAM [48] | 80.50  ±0.18 | 73.14  ±0.13 | 84.07  ±0.12 | 82.35  ±0.19 | 89.80  ±0.23 | 52.09  ±0.06 | 35.64  ±0.27 | 24.58  ±0.09 | 22.55  ±0.06
PASTEL [49] | 80.91  ±0.36 | 72.73  ±0.26 | — | 83.24  ±0.85 | 89.10  ±0.41 | — | 47.12  ±2.82 | 33.15  ±0.66 | 27.56  ±1.04
TOPOAUC [8] | 79.27  ±0.52 | 70.08  ±0.83 | — | 75.35  ±1.32 | 87.10  ±0.98 | — | 33.39  ±2.09 | 22.86  ±0.36 | 22.56  ±0.18
HyperIMBA [12] | 79.81  ±0.78 | 71.78  ±0.40 | 84.75  ±0.30 | 83.43  ±0.65 | 90.65  ±0.14 | — | 38.30  ±2.70 | 29.97  ±1.79 | 25.30  ±2.56

Table D.10: Balanced Accuracy score (% ± standard deviation) of node
classification on manipulated global topology-imbalanced graph datasets with
changing imbalance levels over 10 runs. “—” denotes out of memory or time
limit. Best results are shown in bold and the runner-ups are underlined.

Algorithm |  Cora 0.81 |  CiteSeer 0.74 |  PubMed 0.80 |  Computers 0.78 |  Photo 0.82 |  ogbn-arXiv 0.65 |  Chameleon 0.23 |  Squirrel 0.22 |  Actor 0.22
---|---|---|---|---|---|---|---|---|---
Imbalance Ratio: Low
GCN (bb.) [21] | 82.78  ±0.52 | 67.45  ±0.81 | 85.17  ±0.15 | 85.09  ±1.63 | 89.28  ±1.00 | 36.76  ±0.20 | 38.28  ±0.50 | 25.14  ±0.57 | 23.78  ±0.63
ReNode [7] | 82.89  ±0.82 | 68.52  ±1.14 | 84.52  ±0.11 | 86.93  ±0.83 | 90.03  ±0.51 | 36.79  ±0.18 | 38.02  ±0.50 | 25.36  ±0.49 | 24.04  ±0.39
TAM [48] | 82.49  ±0.11 | 70.97  ±0.13 | 84.71  ±0.06 | 89.91  ±0.08 | 91.81  ±0.13 | 39.96  ±0.05 | 39.16  ±0.14 | 25.63  ±0.12 | 24.25  ±0.19
PASTEL [49] | 83.46  ±0.32 | 71.17  ±0.28 | — | 90.41  ±0.38 | 93.56  ±0.11 | — | 54.27  ±1.18 | 34.02  ±0.57 | 26.89  ±0.43
TOPOAUC [8] | 83.15  ±0.26 | 68.07  ±0.21 | — | 76.90  ±4.12 | 87.93  ±3.60 | — | 38.16  ±0.65 | 23.51  ±0.78 | 23.96  ±0.33
HyperIMBA [12] | 82.32  ±0.41 | 70.75  ±0.56 | 86.45  ±0.11 | 91.54  ±0.30 | 92.36  ±0.16 | — | 43.39  ±1.43 | 32.68  ±0.66 | 28.45  ±3.43
Imbalance Ratio: High
GCN (bb.) [21] | 81.99  ±0.51 | 64.66  ±0.91 | 84.22  ±0.13 | 83.42  ±1.65 | 87.36  ±1.02 | 34.78  ±0.21 | 34.75  ±0.67 | 23.27  ±0.82 | 22.52  ±0.42
ReNode [7] | 82.28  ±0.71 | 66.04  ±0.52 | 83.85  ±0.09 | 85.43  ±0.84 | 88.10  ±0.52 | 34.75  ±0.19 | 33.87  ±0.77 | 23.80  ±0.59 | 22.68  ±0.37
TAM [48] | 82.87  ±0.13 | 69.81  ±0.11 | 84.59  ±0.08 | 87.88  ±0.09 | 89.70  ±0.14 | 37.92  ±0.06 | 36.18  ±0.35 | 24.58  ±0.09 | 23.15  ±0.12
PASTEL [49] | 83.36  ±0.20 | 69.71  ±0.23 | — | 88.92  ±0.39 | 91.40  ±0.12 | — | 47.41  ±2.27 | 33.15  ±0.66 | 25.55  ±0.57
TOPOAUC [8] | 82.28  ±0.35 | 65.82  ±1.20 | — | 74.75  ±4.13 | 86.00  ±3.65 | — | 34.45  ±1.56 | 22.85  ±0.36 | 23.27  ±0.26
HyperIMBA [12] | 82.54  ±0.76 | 68.97  ±0.38 | 85.64  ±0.12 | 89.74  ±0.31 | 90.25  ±0.17 | — | 38.00  ±3.16 | 29.96  ±1.79 | 26.77  ±2.45

Table D.11: Macro-F1 score (% ± standard deviation) of node classification on
manipulated global topology-imbalanced graph datasets with changing imbalance
levels over 10 runs. “—” denotes out of memory or time limit. The best results
are shown in bold and the runner-ups are underlined.

Algorithm |  Cora 0.81 |  CiteSeer 0.74 |  PubMed 0.80 |  Computers 0.78 |  Photo 0.82 |  ogbn-arXiv 0.65 |  Chameleon 0.23 |  Squirrel 0.22 |  Actor 0.22
---|---|---|---|---|---|---|---|---|---
Imbalance Ratio: Low
GCN (bb.) [21] | 79.45  ±0.73 | 66.81  ±1.04 | 83.54  ±0.19 | 64.78  ±2.90 | 84.82  ±1.48 | 33.94  ±0.21 | 36.69  ±0.65 | 24.85  ±0.65 | 23.13  ±0.55
ReNode [7] | 80.26  ±0.38 | 68.21  ±0.81 | 82.98  ±0.12 | 68.61  ±1.47 | 86.14  ±0.66 | 33.88  ±0.17 | 36.60  ±0.50 | 24.75  ±0.61 | 23.33  ±0.28
TAM [48] | 79.01  ±0.24 | 70.30  ±0.13 | 83.22  ±0.08 | 75.36  ±0.22 | 88.34  ±0.22 | 36.75  ±0.05 | 36.45  ±0.19 | 23.59  ±0.27 | 23.44  ±0.20
PASTEL [49] | 80.79  ±0.33 | 70.62  ±0.32 | — | 73.94  ±1.06 | 88.17  ±0.41 | — | 53.30  ±1.30 | 33.54  ±0.69 | 26.34  ±0.23
TOPOAUC [8] | 79.75  ±0.63 | 68.01  ±1.03 | — | 60.13  ±3.52 | 84.39  ±4.10 | — | 36.76  ±1.01 | 21.50  ±1.71 | 22.76  ±0.70
HyperIMBA [12] | 78.85  ±0.66 | 69.96  ±0.53 | 84.16  ±0.26 | 73.55  ±0.72 | 89.45  ±0.21 | — | 42.83  ±1.43 | 30.26  ±1.87 | 26.41  ±3.17
Imbalance Ratio: High
GCN (bb.) [21] | 78.12  ±1.02 | 64.20  ±1.32 | 82.55  ±0.15 | 63.54  ±2.95 | 82.92  ±1.50 | 31.85  ±0.22 | 32.39  ±1.15 | 22.36  ±1.62 | 21.66  ±0.48
ReNode [7] | 78.80  ±1.23 | 65.50  ±0.69 | 82.08  ±0.11 | 66.12  ±1.48 | 84.20  ±0.67 | 31.90  ±0.18 | 30.82  ±1.71 | 22.77  ±1.09 | 21.69  ±0.51
TAM [48] | 79.34  ±0.23 | 69.13  ±0.11 | 83.17  ±0.11 | 73.25  ±0.23 | 86.25  ±0.23 | 34.68  ±0.06 | 33.95  ±0.38 | 22.52  ±0.17 | 22.10  ±0.06
PASTEL [49] | 79.37  ±0.33 | 68.99  ±0.25 | — | 72.45  ±1.07 | 86.25  ±0.42 | — | 46.59  ±3.16 | 31.95  ±1.06 | 25.11  ±0.67
TOPOAUC [8] | 78.24  ±0.42 | 65.48  ±1.05 | — | 58.54  ±3.54 | 82.50  ±4.15 | — | 29.95  ±3.52 | 21.06  ±1.40 | 22.15  ±0.18
HyperIMBA [12] | 78.44  ±0.99 | 68.24  ±0.30 | 83.83  ±0.33 | 71.87  ±0.73 | 87.40  ±0.22 | — | 37.25  ±2.98 | 28.82  ±2.72 | 24.45  ±2.46

Table D.12: AUC-ROC score (% ± standard deviation) of node classification on
manipulated global topology-imbalanced graph datasets with changing imbalance
levels over 10 runs. “—” denotes out of memory or time limit. The best results
are shown in bold and the runner-ups are underlined.

Algorithm |  Cora 0.81 |  CiteSeer 0.74 |  PubMed 0.80 |  Computers 0.78 |  Photo 0.82 |  ogbn-arXiv 0.65 |  Chameleon 0.23 |  Squirrel 0.22 |  Actor 0.22
---|---|---|---|---|---|---|---|---|---
Imbalance Ratio: Low
GCN (bb.) [21] | 94.82  ±0.72 | 88.43  ±1.03 | 94.16  ±0.15 | 94.98  ±1.18 | 93.61  ±1.67 | 88.49  ±0.14 | 66.27  ±0.87 | 54.98  ±0.49 | 54.74  ±0.22
ReNode [7] | 95.16  ±0.67 | 88.41  ±0.99 | 94.06  ±0.40 | 94.91  ±1.26 | 93.97  ±1.60 | 88.42  ±0.16 | 66.08  ±0.30 | 55.21  ±0.47 | 54.83  ±0.20
TAM [48] | 96.75  ±0.04 | 91.87  ±0.07 | 94.86  ±0.01 | 98.17  ±0.01 | 99.01  ±0.01 | 92.30  ±0.02 | 65.00  ±0.37 | 55.10  ±0.10 | 55.44  ±0.24
PASTEL [49] | 97.05  ±0.07 | 92.90  ±0.13 | — | 98.45  ±0.03 | 99.28  ±0.03 | — | 80.43  ±0.46 | 63.47  ±0.47 | 59.43  ±0.30
TOPOAUC [8] | 97.07  ±0.20 | 90.67  ±0.67 | — | 92.28  ±2.62 | 98.54  ±0.14 | — | 65.74  ±0.47 | 52.72  ±0.34 | 55.21  ±0.60
HyperIMBA [12] | 96.19  ±0.19 | 91.50  ±0.51 | 95.31  ±0.11 | 98.39  ±0.06 | 98.71  ±0.09 | — | 68.48  ±2.94 | 60.29  ±1.42 | 59.92  ±3.31
Imbalance Ratio: High
GCN (bb.) [21] | 94.97  ±0.67 | 87.95  ±1.04 | 93.02  ±0.17 | 93.05  ±1.22 | 91.45  ±1.70 | 86.43  ±0.15 | 62.31  ±1.16 | 53.67  ±0.33 | 53.17  ±0.29
ReNode [7] | 95.00  ±0.78 | 87.86  ±1.00 | 93.23  ±0.21 | 93.75  ±1.27 | 92.15  ±1.62 | 86.42  ±0.17 | 61.68  ±1.15 | 54.15  ±0.49 | 53.02  ±0.18
TAM [48] | 96.78  ±0.13 | 92.04  ±0.12 | 94.88  ±0.02 | 96.23  ±0.02 | 97.20  ±0.02 | 90.25  ±0.03 | 62.91  ±0.62 | 54.27  ±0.06 | 53.49  ±0.06
PASTEL [49] | 97.31  ±0.04 | 92.65  ±0.10 | — | 96.75  ±0.04 | 97.10  ±0.04 | — | 76.49  ±0.97 | 63.78  ±0.40 | 57.70  ±0.37
TOPOAUC [8] | 96.54  ±0.22 | 89.88  ±0.25 | — | 90.89  ±2.63 | 96.40  ±0.15 | — | 60.37  ±1.82 | 52.77  ±0.21 | 53.96  ±0.21
HyperIMBA [12] | 96.57  ±0.30 | 92.23  ±0.32 | 94.95  ±0.13 | 96.85  ±0.07 | 96.55  ±0.10 | — | 64.57  ±1.44 | 58.83  ±2.05 | 57.20  ±2.58

#####  D.1.4 Performance of Graph-Level Class-Imbalanced Algorithms

Table D.13: Accuracy score (% ± standard deviation) of graph classification on
manipulated class-imbalanced graph datasets with changing imbalance levels
over 10 runs. “—” denotes out of memory or time limit. The best results are
shown in bold and the runner-ups are underlined.

Algorithm | PTC-MR | FRANKENSTEIN | PROTEINS | D&D | IMDB-B | REDDIT-B | COLLAB
---|---|---|---|---|---|---|---
$\bm{\rho}=$ 1 (Balanced)
GIN (bb.) [59] | 50.43  ±2.69 | 64.27  ±2.47 | 65.34  ±2.72 | 64.04  ±3.79 | 66.05  ±2.57 | 76.66  ±4.80 | 65.31  ±3.25
G2GNN [54] | 53.70  ±3.87 | 63.63  ±1.16 | 65.50  ±2.69 | 66.07  ±2.27 | 61.91  ±3.77 | 72.34  ±2.76 | 53.82  ±2.26
TopoImb [68] | 50.91  ±2.18 | 61.45  ±3.74 | 55.04  ±5.13 | 66.57  ±3.81 | 66.28  ±1.85 | 73.99  ±1.18 | 65.92  ±1.36
DataDec [64] | 54.05  ±4.85 | 66.90  ±3.36 | 65.24  ±4.06 | 64.46  ±1.88 | 64.09  ±5.75 | 79.29  ±8.18 | 72.24  ±0.19
ImGKB [50] | 53.48  ±3.50 | 52.54  ±6.05 | 69.85  ±1.95 | 65.45  ±2.88 | 50.16  ±0.34 | 50.24  ±0.29 | 39.34  ±10.88
$\bm{\rho}=$ 20 (Low)
GIN (bb.) [59] | 47.83  ±2.95 | 63.38  ±1.93 | 55.38  ±3.57 | 51.05  ±5.07 | 62.31  ±3.99 | 61.10  ±4.86 | 65.01  ±1.33
G2GNN [54] | 51.88  ±6.23 | 61.13  ±1.05 | 63.61  ±5.03 | 56.29  ±7.30 | 63.87  ±4.64 | 69.58  ±3.59 | 62.05  ±3.06
TopoImb [68] | 44.86  ±3.52 | 49.49  ±7.14 | 52.12  ±10.51 | 49.97  ±7.24 | 59.95  ±5.19 | 59.67  ±7.30 | 65.88  ±0.75
DataDec [64] | 55.72  ±2.88 | 67.99  ±0.75 | 66.58  ±1.35 | 63.51  ±1.62 | 67.92  ±3.37 | 78.39  ±5.01 | 71.48  ±1.03
ImGKB [50] | 50.11  ±5.95 | 40.83  ±0.02 | 66.60  ±2.64 | 65.85  ±3.70 | 47.74  ±0.29 | 48.57  ±2.14 | 51.21  ±0.10
$\bm{\rho}=$ 100 (High)
GIN (bb.) [59] | 39.42  ±1.87 | 56.02  ±1.43 | 42.50  ±2.05 | 41.54  ±6.57 | 53.57  ±3.21 | 55.56  ±7.85 | 62.00  ±3.08
G2GNN [54] | 46.52  ±9.94 | 55.41  ±3.91 | 52.97  ±13.44 | 55.38  ±15.60 | 59.44  ±6.49 | 63.22  ±4.67 | 62.61  ±1.14
TopoImb [68] | 39.42  ±1.24 | 46.45  ±6.77 | 39.23  ±4.28 | 39.12  ±1.62 | 47.75  ±3.73 | 51.58  ±4.69 | 64.19  ±1.77
DataDec [64] | 58.69  ±3.10 | 67.82  ±1.88 | 61.99  ±7.15 | 65.77  ±2.71 | 66.30  ±6.70 | 77.72  ±5.12 | 71.50  ±1.15
ImGKB [50] | 44.24  ±5.65 | 38.34  ±0.01 | 61.46  ±10.25 | 59.99  ±7.57 | 47.08  ±3.72 | 51.25  ±5.10 | 50.20  ±0.06

Table D.14: Balanced Accuracy score (% ± standard deviation) of graph
classification on manipulated class-imbalanced graph datasets with changing
imbalance levels over 10 runs. “—” denotes out of memory or time limit. The
best results are shown in bold and the runner-ups are underlined.

Algorithm | PTC-MR | FRANKENSTEIN | PROTEINS | D&D | IMDB-B | REDDIT-B | COLLAB
---|---|---|---|---|---|---|---
$\bm{\rho}=$ 1 (Balanced)
GIN (bb.) [59] | 51.40  ±1.64 | 64.33  ±2.20 | 64.90  ±1.51 | 63.37  ±3.26 | 66.05  ±2.57 | 76.66  ±4.80 | 72.99  ±1.83
G2GNN [54] | 53.42  ±3.72 | 63.55  ±1.22 | 64.39  ±2.21 | 63.79  ±2.13 | 61.91  ±3.77 | 72.34  ±2.76 | 64.17  ±0.51
TopoImb [68] | 53.99  ±2.19 | 60.81  ±2.83 | 59.71  ±2.03 | 67.19  ±2.46 | 66.28  ±1.85 | 73.99  ±1.18 | 51.93  ±2.88
DataDec [64] | 53.70  ±4.25 | 65.06  ±5.28 | 62.39  ±2.38 | 62.96  ±1.21 | 64.22  ±5.73 | 79.80  ±7.38 | 62.31  ±1.96
ImGKB [50] | 53.34  ±3.61 | 49.98  ±0.06 | 68.09  ±2.49 | 62.33  ±4.38 | 49.99  ±0.47 | 50.24  ±0.29 | 33.38  ±0.10
$\bm{\rho}=$ 20 (Low)
GIN (bb.) [59] | 51.36  ±2.25 | 61.90  ±2.13 | 60.39  ±2.22 | 57.33  ±3.16 | 63.54  ±3.46 | 62.89  ±4.61 | 47.03  ±1.45
G2GNN [54] | 52.75  ±2.14 | 63.31  ±1.14 | 66.18  ±3.06 | 61.09  ±4.11 | 64.28  ±5.02 | 70.26  ±3.41 | 60.76  ±2.04
TopoImb [68] | 50.44  ±3.75 | 56.57  ±5.30 | 59.88  ±6.33 | 58.33  ±4.40 | 61.14  ±4.56 | 61.34  ±6.80 | 48.95  ±1.64
DataDec [64] | 53.42  ±2.33 | 66.10  ±1.22 | 61.54  ±2.33 | 61.27  ±1.04 | 67.95  ±2.77 | 78.68  ±4.93 | 68.71  ±1.11
ImGKB [50] | 51.61  ±3.12 | 50.01  ±0.02 | 64.72  ±5.37 | 63.39  ±1.76 | 50.23  ±0.28 | 50.07  ±0.15 | 33.33  ±0.00
$\bm{\rho}=$ 100 (High)
GIN (bb.) [59] | 47.89  ±2.12 | 54.66  ±1.53 | 53.30  ±1.63 | 52.47  ±4.58 | 57.46  ±2.77 | 59.54  ±7.11 | 44.67  ±2.98
G2GNN [54] | 50.76  ±1.78 | 60.38  ±1.91 | 51.32  ±6.16 | 53.17  ±2.90 | 61.85  ±5.36 | 65.97  ±4.07 | 54.91  ±2.09
TopoImb [68] | 49.99  ±0.93 | 55.82  ±4.93 | 53.96  ±2.78 | 52.05  ±1.31 | 52.82  ±3.06 | 55.87  ±4.09 | 47.98  ±1.65
DataDec [64] | 55.22  ±3.81 | 65.24  ±2.16 | 60.22  ±3.13 | 61.60  ±2.60 | 66.30  ±4.93 | 77.77  ±5.49 | 68.99  ±2.04
ImGKB [50] | 51.38  ±3.53 | 50.00  ±0.01 | 64.48  ±5.90 | 59.14  ±4.10 | 50.07  ±0.35 | 50.28  ±0.23 | 33.33  ±0.00

Table D.15: Macro-F1 score (% ± standard deviation) of graph classification on
manipulated class-imbalanced graph datasets with changing imbalance levels
over 10 runs. “—” denotes out of memory or time limit. The best results are
shown in bold and the runner-ups are underlined.

Algorithm | PTC-MR | FRANKENSTEIN | PROTEINS | D&D | IMDB-B | REDDIT-B | COLLAB
---|---|---|---|---|---|---|---
$\bm{\rho}=$ 1 (Balanced)
GIN (bb.) [59] | 48.85  ±3.33 | 63.86  ±2.39 | 63.98  ±2.09 | 59.87  ±7.24 | 65.24  ±3.21 | 76.20  ±5.00 | 60.83  ±3.61
G2GNN [54] | 52.88  ±3.70 | 63.28  ±1.13 | 63.89  ±2.39 | 63.31  ±2.42 | 60.99  ±3.50 | 71.74  ±3.14 | 46.71  ±2.55
TopoImb [68] | 48.33  ±3.70 | 58.58  ±5.21 | 53.13  ±5.72 | 65.72  ±3.45 | 65.85  ±2.29 | 73.41  ±0.01 | 51.32  ±4.63
DataDec [64] | 52.98  ±4.65 | 63.64  ±9.26 | 62.20  ±3.28 | 62.83  ±1.20 | 62.42  ±8.07 | 79.02  ±8.63 | 63.82  ±1.02
ImGKB [50] | 50.36  ±5.89 | 34.59  ±2.65 | 67.98  ±2.43 | 61.06  ±7.96 | 35.27  ±4.74 | 33.97  ±0.42 | 18.66  ±3.43
$\bm{\rho}=$ 20 (Low)
GIN (bb.) [59] | 46.63  ±2.95 | 61.27  ±2.51 | 55.20  ±3.70 | 49.89  ±6.19 | 59.66  ±5.94 | 56.10  ±6.75 | 37.64  ±1.08
G2GNN [54] | 47.64  ±7.63 | 61.11  ±1.06 | 62.89  ±4.70 | 55.34  ±8.20 | 61.37  ±8.64 | 69.03  ±3.78 | 55.48  ±2.78
TopoImb [68] | 40.26  ±2.06 | 43.64  ±11.61 | 49.66  ±12.86 | 47.37  ±9.53 | 56.78  ±8.24 | 54.07  ±11.22 | 47.31  ±0.03
DataDec [64] | 52.31  ±3.50 | 66.22  ±1.25 | 61.66  ±2.33 | 61.12  ±1.22 | 67.42  ±3.69 | 77.96  ±5.66 | 68.49  ±0.60
ImGKB [50] | 44.62  ±8.86 | 29.05  ±0.08 | 62.49  ±8.12 | 62.91  ±2.34 | 32.70  ±0.62 | 32.81  ±1.21 | 22.58  ±0.03
$\bm{\rho}=$ 100 (High)
GIN (bb.) [59] | 35.14  ±4.01 | 46.81  ±3.33 | 41.20  ±2.65 | 38.83  ±8.36 | 47.51  ±5.47 | 48.74  ±11.66 | 36.37  ±0.93
G2GNN [54] | 37.35  ±7.10 | 54.73  ±4.33 | 44.16  ±10.15 | 42.22  ±11.10 | 56.79  ±9.27 | 61.15  ±6.30 | 50.73  ±4.21
TopoImb [68] | 32.16  ±3.27 | 40.55  ±10.82 | 34.48  ±6.61 | 34.24  ±2.40 | 36.64  ±6.35 | 41.81  ±9.90 | 45.32  ±0.02
DataDec [64] | 54.76  ±4.61 | 64.94  ±2.97 | 58.47  ±4.92 | 61.67  ±2.67 | 64.82  ±8.14 | 77.39  ±5.38 | 68.87  ±1.57
ImGKB [50] | 41.35  ±7.92 | 27.73  ±0.04 | 59.75  ±11.28 | 57.16  ±5.54 | 32.23  ±1.61 | 34.31  ±2.68 | 22.28  ±0.02

Table D.16: AUC-ROC score (% ± standard deviation) of graph classification on
manipulated class-imbalanced graph datasets with changing imbalance levels
over 10 runs. “—” denotes out of memory or time limit. The best results are
shown in bold and the runner-ups are underlined.

Algorithm | PTC-MR | FRANKENSTEIN | PROTEINS | D&D | IMDB-B | REDDIT-B | COLLAB
---|---|---|---|---|---|---|---
$\bm{\rho}=$ 1 (Balanced)
GIN (bb.) [59] | 52.26  ±2.95 | 69.20  ±2.35 | 67.91  ±2.87 | 66.54  ±5.28 | 73.99  ±2.41 | 87.61  ±4.35 | 86.80  ±1.38
G2GNN [54] | 54.55  ±5.56 | 68.03  ±1.39 | 67.09  ±3.07 | 70.05  ±2.41 | 64.87  ±4.48 | 80.22  ±4.01 | 79.90  ±0.80
TopoImb [68] | 56.93  ±4.29 | 69.09  ±1.17 | 69.33  ±4.09 | 72.86  ±1.46 | 74.83  ±1.01 | 81.49  ±3.03 | 85.12  ±0.39
DataDec [64] | 54.57  ±6.02 | 72.65  ±3.55 | 68.80  ±4.16 | 68.18  ±1.32 | 72.25  ±5.65 | 81.26  ±13.78 | 87.29  ±0.32
ImGKB [50] | 54.09  ±5.28 | 54.78  ±2.66 | 73.47  ±2.00 | 66.54  ±2.08 | 50.60  ±1.23 | 74.36  ±5.01 | 50.29  ±0.86
$\bm{\rho}=$ 20 (Low)
GIN (bb.) [59] | 51.28  ±4.16 | 68.74  ±2.22 | 59.21  ±3.70 | 54.13  ±6.72 | 74.38  ±2.48 | 84.08  ±4.85 | 86.05  ±1.11
G2GNN [54] | 51.90  ±3.85 | 68.70  ±1.13 | 69.59  ±3.54 | 64.49  ±5.43 | 69.02  ±3.60 | 77.97  ±4.62 | 78.15  ±2.04
TopoImb [68] | 50.82  ±3.94 | 67.96  ±2.26 | 66.77  ±5.44 | 67.76  ±4.85 | 72.61  ±2.10 | 83.30  ±3.79 | 86.31  ±1.42
DataDec [64] | 53.49  ±1.94 | 73.98  ±0.59 | 69.32  ±1.81 | 67.05  ±1.47 | 75.40  ±3.23 | 81.00  ±8.17 | 85.68  ±2.32
ImGKB [50] | 52.89  ±4.84 | 53.59  ±1.12 | 72.57  ±1.37 | 68.08  ±2.00 | 51.06  ±1.08 | 76.25  ±3.29 | 50.42  ±0.97
$\bm{\rho}=$ 100 (High)
GIN (bb.) [59] | 47.04  ±3.22 | 64.26  ±4.79 | 59.00  ±2.60 | 47.06  ±5.01 | 65.96  ±9.53 | 80.58  ±3.45 | 81.04  ±3.44
G2GNN [54] | 49.32  ±4.07 | 66.60  ±1.48 | 52.10  ±7.10 | 60.76  ±4.90 | 65.79  ±7.00 | 72.55  ±5.64 | 75.67  ±1.51
TopoImb [68] | 48.09  ±3.94 | 69.48  ±1.14 | 65.62  ±3.19 | 61.49  ±5.30 | 69.12  ±7.15 | 80.08  ±5.47 | 82.28  ±2.86
DataDec [64] | 57.66  ±5.55 | 73.51  ±1.01 | 64.35  ±6.86 | 69.11  ±3.67 | 74.89  ±4.11 | 82.59  ±6.05 | 87.03  ±1.21
ImGKB [50] | 52.80  ±5.19 | 54.03  ±2.17 | 71.98  ±2.36 | 63.79  ±4.04 | 51.04  ±1.57 | 71.65  ±6.48 | 50.05  ±0.63

Table D.17: Accuracy score (% ± standard deviation) of graph classification on
manipulated class-imbalanced graph datasets with changing imbalance levels
over 10 runs. “—” denotes out of memory or time limit. The best results are
shown in bold and the runner-ups are underlined.

Algorithm | PTC-MR | FRANKENSTEIN | PROTEINS | D&D | IMDB-B | REDDIT-B | COLLAB
---|---|---|---|---|---|---|---
$\bm{\rho}=$ 1 (Balanced)
GCN (bb.) [21] | 48.62  ±7.12 | 52.67  ±6.11 | 65.44  ±2.73 | 63.97  ±4.09 | 59.76  ±1.78 | 66.65  ±1.06 | 61.23  ±3.38
G2GNN [54] | 44.35  ±4.32 | 52.10  ±4.27 | 68.82  ±2.83 | 61.47  ±7.70 | 58.35  ±3.47 | 67.02  ±2.55 | 49.49  ±3.18
TopoImb [68] | 50.61  ±6.39 | 48.03  ±5.90 | 57.41  ±5.95 | 56.13  ±4.61 | 49.52  ±1.01 | 58.62  ±6.52 | 58.63  ±1.93
DataDec [64] | 54.23  ±4.16 | 63.46  ±4.36 | 67.25  ±5.25 | 63.10  ±2.62 | 58.20  ±4.05 | 69.08  ±4.49 | 69.03  ±1.89
ImGKB [50] | 52.83  ±5.45 | 53.97  ±5.28 | 64.57  ±9.42 | 64.93  ±4.44 | 50.15  ±0.39 | 50.29  ±0.19 | 40.44  ±11.33
$\bm{\rho}=$ 20 (Low)
GCN (bb.) [21] | 43.84  ±7.03 | 48.59  ±9.57 | 54.01  ±2.86 | 58.32  ±1.51 | 49.06  ±2.17 | 61.85  ±3.89 | 53.81  ±1.88
G2GNN [54] | 47.86  ±9.03 | 57.28  ±1.85 | 69.42  ±1.80 | 65.65  ±5.41 | 53.11  ±3.97 | 66.02  ±2.08 | 54.57  ±3.30
TopoImb [68] | 45.90  ±6.41 | 40.71  ±0.33 | 38.27  ±5.28 | 44.63  ±4.82 | 49.75  ±4.81 | 54.35  ±3.13 | 57.72  ±1.71
DataDec [64] | 55.86  ±2.49 | 63.28  ±3.54 | 64.23  ±7.74 | 64.66  ±2.04 | 57.06  ±5.97 | 66.45  ±5.38 | 71.26  ±0.91
ImGKB [50] | 49.49  ±5.12 | 40.82  ±0.02 | 68.44  ±2.58 | 67.44  ±3.50 | 47.65  ±0.23 | 48.58  ±2.15 | 51.21  ±0.10
$\bm{\rho}=$ 100 (High)
GCN (bb.) [21] | 40.58  ±7.61 | 43.03  ±9.39 | 37.34  ±3.35 | 42.48  ±2.61 | 45.09  ±0.18 | 54.39  ±5.16 | 50.47  ±0.38
G2GNN [54] | 41.78  ±7.61 | 49.50  ±11.24 | 61.27  ±6.39 | 44.59  ±4.72 | 56.40  ±1.71 | 65.08  ±3.08 | 58.02  ±3.29
TopoImb [68] | 40.17  ±2.21 | 38.50  ±0.35 | 33.21  ±0.05 | 36.50  ±1.44 | 46.18  ±3.06 | 52.21  ±3.56 | 61.40  ±2.44
DataDec [64] | 55.41  ±3.37 | 63.82  ±6.75 | 66.08  ±7.51 | 65.07  ±2.40 | 58.58  ±5.07 | 65.56  ±8.61 | 70.48  ±0.49
ImGKB [50] | 45.98  ±8.71 | 38.34  ±0.02 | 65.09  ±2.81 | 58.21  ±10.60 | 46.06  ±2.74 | 51.23  ±5.09 | 50.20  ±0.06

Table D.18: Balanced Accuracy score (% ± standard deviation) of graph
classification on manipulated class-imbalanced graph datasets with changing
imbalance levels over 10 runs. “—” denotes out of memory or time limit. The
best results are shown in bold and the runner-ups are underlined.

Algorithm | PTC-MR | FRANKENSTEIN | PROTEINS | D&D | IMDB-B | REDDIT-B | COLLAB
---|---|---|---|---|---|---|---
$\bm{\rho}=$ 1 (Balanced)
GCN (bb.) [21] | 50.07  ±0.23 | 50.00  ±0.02 | 64.60  ±2.26 | 62.63  ±2.06 | 59.76  ±1.78 | 66.65  ±1.06 | 69.44  ±2.08
G2GNN [54] | 50.02  ±0.06 | 51.82  ±1.81 | 67.39  ±1.76 | 60.38  ±5.83 | 58.35  ±3.47 | 67.02  ±2.55 | 61.96  ±0.90
TopoImb [68] | 53.71  ±2.88 | 51.13  ±1.64 | 61.24  ±5.25 | 60.56  ±2.30 | 49.71  ±0.34 | 58.68  ±6.48 | 44.78  ±3.02
DataDec [64] | 54.36  ±3.61 | 62.09  ±3.25 | 63.92  ±4.14 | 61.41  ±2.42 | 58.11  ±3.96 | 69.08  ±4.38 | 62.12  ±4.15
ImGKB [50] | 53.03  ±3.56 | 49.98  ±0.06 | 65.28  ±5.36 | 62.84  ±2.56 | 50.15  ±0.39 | 50.29  ±0.19 | 33.35  ±0.01
$\bm{\rho}=$ 20 (Low)
GCN (bb.) [21] | 49.69  ±0.68 | 50.73  ±2.05 | 59.49  ±1.56 | 60.53  ±1.43 | 51.35  ±1.88 | 63.51  ±3.57 | 37.97  ±2.15
G2GNN [54] | 49.73  ±0.87 | 53.76  ±2.16 | 68.31  ±1.72 | 65.61  ±2.52 | 53.84  ±3.33 | 66.54  ±2.09 | 61.19  ±1.44
TopoImb [68] | 51.60  ±3.14 | 49.98  ±0.02 | 51.14  ±2.23 | 54.87  ±2.95 | 48.94  ±4.07 | 56.51  ±2.84 | 46.73  ±0.87
DataDec [64] | 54.50  ±1.74 | 59.94  ±3.73 | 61.80  ±4.57 | 62.01  ±1.75 | 56.87  ±5.73 | 67.02  ±5.12 | 67.53  ±2.03
ImGKB [50] | 51.70  ±2.33 | 49.99  ±0.02 | 67.46  ±1.22 | 63.70  ±3.66 | 50.14  ±0.22 | 50.08  ±0.16 | 33.34  ±0.01
$\bm{\rho}=$ 100 (High)
GCN (bb.) [21] | 50.36  ±1.14 | 50.30  ±0.61 | 51.78  ±1.94 | 53.22  ±2.13 | 50.08  ±0.16 | 58.47  ±4.64 | 33.99  ±0.32
G2GNN [54] | 49.94  ±1.47 | 50.31  ±0.97 | 65.24  ±4.47 | 54.99  ±3.11 | 58.87  ±1.18 | 65.09  ±3.02 | 53.69  ±3.41
TopoImb [68] | 50.78  ±0.68 | 49.99  ±0.02 | 50.01  ±0.03 | 49.47  ±1.20 | 51.02  ±2.25 | 56.40  ±2.67 | 46.42  ±3.04
DataDec [64] | 53.28  ±2.65 | 58.87  ±3.26 | 63.07  ±5.35 | 60.83  ±2.61 | 58.11  ±4.26 | 66.61  ±6.89 | 67.66  ±1.56
ImGKB [50] | 50.19  ±3.07 | 49.99  ±0.02 | 64.52  ±4.98 | 60.22  ±4.56 | 50.06  ±0.31 | 50.26  ±0.22 | 33.33  ±0.01

Table D.19: Macro-F1 score (% ± standard deviation) of graph classification on
manipulated class-imbalanced graph datasets with changing imbalance levels
over 10 runs. “—” denotes out of memory or time limit. The best results are
shown in bold and the runner-ups are underlined.

Algorithm | PTC-MR | FRANKENSTEIN | PROTEINS | D&D | IMDB-B | REDDIT-B | COLLAB
---|---|---|---|---|---|---|---
$\bm{\rho}=$ 1 (Balanced)
GCN (bb.) [21] | 32.82  ±3.29 | 34.45  ±2.70 | 64.08  ±2.43 | 62.02  ±2.84 | 59.32  ±2.48 | 67.58  ±1.06 | 56.55  ±4.31
G2GNN [54] | 31.29  ±2.68 | 45.92  ±8.09 | 67.11  ±2.26 | 56.99  ±10.85 | 56.41  ±7.64 | 65.63  ±3.26 | 41.15  ±4.18
TopoImb [68] | 45.01  ±8.36 | 37.18  ±7.96 | 56.62  ±6.11 | 55.05  ±4.87 | 33.04  ±0.43 | 50.17  ±12.11 | 40.73  ±3.28
DataDec [64] | 53.24  ±3.23 | 61.26  ±4.55 | 64.05  ±4.48 | 61.35  ±2.55 | 54.26  ±7.60 | 67.37  ±6.20 | 62.14  ±3.48
ImGKB [50] | 48.53  ±8.31 | 35.15  ±2.37 | 62.33  ±11.90 | 62.34  ±3.64 | 33.84  ±0.60 | 33.97  ±0.41 | 18.99  ±3.59
$\bm{\rho}=$ 20 (Low)
GCN (bb.) [21] | 31.49  ±5.35 | 34.14  ±7.63 | 53.81  ±2.94 | 58.06  ±1.46 | 36.70  ±6.23 | 57.56  ±6.17 | 42.17  ±5.55
G2GNN [54] | 33.06  ±4.46 | 51.94  ±5.20 | 67.58  ±1.71 | 64.18  ±4.21 | 45.81  ±10.04 | 65.51  ±2.39 | 47.61  ±4.89
TopoImb [68] | 39.66  ±9.73 | 28.90  ±0.15 | 30.36  ±7.82 | 40.50  ±7.73 | 37.79  ±5.88 | 45.50  ±5.89 | 41.59  ±1.32
DataDec [64] | 54.16  ±1.97 | 57.35  ±6.49 | 60.87  ±6.00 | 61.94  ±1.91 | 50.18  ±11.79 | 64.62  ±6.82 | 67.94  ±1.44
ImGKB [50] | 45.80  ±7.16 | 29.04  ±0.10 | 66.63  ±1.90 | 63.41  ±4.10 | 32.52  ±0.48 | 32.82  ±1.24 | 22.58  ±0.03
$\bm{\rho}=$ 100 (High)
GCN (bb.) [21] | 29.74  ±6.39 | 31.00  ±6.60 | 32.66  ±5.33 | 40.59  ±3.18 | 31.21  ±0.36 | 47.46  ±8.81 | 35.27  ±2.66
G2GNN [54] | 32.13  ±7.08 | 34.53  ±7.98 | 60.58  ±5.98 | 42.79  ±6.25 | 54.41  ±2.63 | 64.77  ±3.25 | 45.03  ±5.63
TopoImb [68] | 32.03  ±3.31 | 27.74  ±0.17 | 24.89  ±0.07 | 31.98  ±1.84 | 33.79  ±6.25 | 44.46  ±6.18 | 42.64  ±3.76
DataDec [64] | 52.48  ±3.00 | 56.32  ±7.38 | 62.23  ±5.92 | 60.89  ±2.60 | 53.87  ±8.76 | 62.46  ±11.54 | 67.68  ±0.43
ImGKB [50] | 39.08  ±8.03 | 27.76  ±0.09 | 61.19  ±7.33 | 55.46  ±11.43 | 31.73  ±0.22 | 34.27  ±2.64 | 22.28  ±0.02

Table D.20: AUC-ROC score (% ± standard deviation) of graph classification on
manipulated class-imbalanced graph datasets with changing imbalance levels
over 10 runs. “—” denotes out of memory or time limit. The best results are
shown in bold and the runner-ups are underlined.

Algorithm | PTC-MR | FRANKENSTEIN | PROTEINS | D&D | IMDB-B | REDDIT-B | COLLAB
---|---|---|---|---|---|---|---
$\bm{\rho}=$ 1 (Balanced)
GCN (bb.) [21] | 49.33  ±7.50 | 47.99  ±6.53 | 67.82  ±1.87 | 67.24  ±2.12 | 63.97  ±2.24 | 75.18  ±0.08 | 82.29  ±1.74
G2GNN [54] | 45.43  ±5.01 | 53.96  ±1.98 | 70.27  ±2.46 | 68.38  ±3.80 | 61.49  ±6.19 | 74.01  ±3.96 | 76.39  ±1.05
TopoImb [68] | 56.98  ±4.51 | 57.57  ±1.02 | 69.62  ±6.65 | 70.29  ±1.96 | 48.80  ±10.38 | 77.48  ±1.84 | 74.54  ±1.33
DataDec [64] | 55.99  ±4.78 | 69.51  ±3.35 | 69.52  ±7.69 | 66.85  ±3.20 | 62.53  ±3.42 | 66.49  ±9.00 | 77.38  ±4.14
ImGKB [50] | 53.61  ±5.87 | 54.93  ±1.84 | 72.75  ±1.17 | 67.82  ±1.50 | 51.83  ±1.56 | 72.98  ±5.95 | 49.92  ±0.89
$\bm{\rho}=$ 20 (Low)
GCN (bb.) [21] | 45.84  ±4.13 | 61.32  ±4.03 | 67.36  ±1.94 | 65.26  ±2.20 | 62.50  ±1.26 | 75.19  ±1.08 | 81.28  ±1.49
G2GNN [54] | 48.93  ±5.12 | 54.45  ±3.61 | 71.85  ±1.86 | 71.03  ±1.85 | 57.06  ±4.74 | 73.96  ±2.66 | 76.39  ±1.05
TopoImb [68] | 55.07  ±4.49 | 57.41  ±1.16 | 72.43  ±5.51 | 72.19  ±3.37 | 50.00  ±10.14 | 77.58  ±0.54 | 77.08  ±0.50
DataDec [64] | 56.27  ±2.77 | 68.73  ±2.50 | 67.18  ±7.60 | 68.13  ±2.14 | 64.08  ±3.48 | 65.24  ±11.34 | 87.01  ±0.67
ImGKB [50] | 52.91  ±3.96 | 54.52  ±2.20 | 71.14  ±3.19 | 68.34  ±2.86 | 51.08  ±0.71 | 76.70  ±3.52 | 50.16  ±0.94
$\bm{\rho}=$ 100 (High)
GCN (bb.) [21] | 44.65  ±4.74 | 46.38  ±5.76 | 65.59  ±1.10 | 64.67  ±1.98 | 56.60  ±8.91 | 76.80  ±2.42 | 77.77  ±2.43
G2GNN [54] | 46.82  ±4.30 | 49.91  ±1.64 | 68.51  ±3.63 | 67.30  ±2.70 | 62.46  ±2.16 | 72.42  ±3.79 | 70.81  ±3.61
TopoImb [68] | 53.31  ±5.12 | 56.71  ±0.63 | 70.74  ±4.14 | 57.78  ±6.66 | 52.42  ±10.28 | 77.07  ±0.24 | 75.96  ±0.51
DataDec [64] | 55.65  ±3.63 | 68.13  ±2.76 | 69.26  ±8.47 | 67.68  ±2.86 | 63.17  ±4.96 | 64.92  ±15.31 | 87.21  ±0.35
ImGKB [50] | 51.01  ±4.09 | 53.74  ±0.93 | 70.71  ±1.27 | 65.42  ±3.01 | 51.05  ±1.00 | 71.01  ±5.58 | 50.01  ±0.58

#####  D.1.5 Performance of Graph-Level Topology-Imbalanced Algorithms

Table D.21: Accuracy score (% ± standard deviation) of graph classification on
manipulated topology-imbalanced graph datasets with changing imbalance levels
over 10 runs. “—” denotes out of memory or time limit. The best results are
shown in bold.

Algorithm | PTC-MR | FRANKENSTEIN | PROTEINS | D&D | IMDB-B | REDDIT-B | COLLAB
---|---|---|---|---|---|---|---
Imbalance Ratio: Low
GIN (bb.) [59] | 52.17  ±4.36 | 54.96  ±1.00 | 63.58  ±1.76 | 65.01  ±0.69 | 66.38  ±4.27 | 67.41  ±2.32 | 64.34  ±3.55
SOLT-GNN [28] | 47.54  ±4.33 | 59.98  ±1.11 | 65.56  ±4.83 | 63.78  ±1.06 | 64.20  ±5.46 | 49.57  ±6.78 | 61.79  ±2.09
TopoImb [68] | 49.71  ±1.98 | 53.13  ±0.45 | 61.19  ±4.61 | 65.16  ±1.76 | 66.00  ±2.41 | 69.47  ±3.70 | 62.71  ±2.42
Imbalance Ratio: Mid
GIN (bb.) [59] | 51.38  ±6.78 | 54.82  ±2.26 | 62.14  ±2.43 | 61.46  ±2.43 | 65.08  ±5.78 | 68.32  ±1.77 | 65.84  ±3.12
SOLT-GNN [28] | 53.04  ±3.91 | 68.71  ±1.60 | 71.95  ±2.36 | 63.33  ±1.86 | 69.38  ±1.23 | 73.51  ±1.14 | 69.69  ±2.45
TopoImb [68] | 51.59  ±4.30 | 54.52  ±0.87 | 64.03  ±4.43 | 65.99  ±1.25 | 68.10  ±0.87 | 71.54  ±0.75 | 68.68  ±1.34
Imbalance Ratio: High
GIN (bb.) [59] | 48.41  ±7.07 | 53.99  ±7.96 | 58.00  ±4.19 | 60.68  ±6.89 | 62.60  ±3.82 | 67.41  ±2.23 | 67.05  ±2.46
SOLT-GNN [28] | 51.74  ±5.25 | 67.88  ±2.37 | 72.04  ±2.18 | 64.97  ±3.24 | 65.03  ±4.12 | 60.24  ±2.11 | 67.12  ±3.28
TopoImb [68] | 51.96  ±1.16 | 56.32  ±0.61 | 54.89  ±13.58 | 64.16  ±2.96 | 66.75  ±0.91 | 69.14  ±4.83 | 67.52  ±0.77

Table D.22: Balanced Accuracy score (% ± standard deviation) of graph
classification on manipulated topology-imbalanced graph datasets with changing
imbalance levels over 10 runs. “—” denotes out of memory or time limit. The
best results are shown in bold.

Algorithm | PTC-MR | FRANKENSTEIN | PROTEINS | D&D | IMDB-B | REDDIT-B | COLLAB
---|---|---|---|---|---|---|---
Imbalance Ratio: Low
GIN (bb.) [59] | 51.08  ±2.07 | 55.22  ±1.39 | 59.76  ±1.78 | 63.46  ±0.92 | 66.38  ±4.27 | 67.41  ±2.32 | 64.73  ±5.42
SOLT-GNN [28] | 45.47  ±2.10 | 63.58  ±0.82 | 66.60  ±3.25 | 62.58  ±0.61 | 64.20  ±5.46 | 49.57  ±6.78 | 70.23  ±1.56
TopoImb [68] | 50.07  ±2.77 | 54.44  ±0.41 | 63.87  ±1.68 | 67.24  ±1.53 | 66.00  ±2.41 | 69.47  ±3.70 | 71.56  ±1.68
Imbalance Ratio: Mid
GIN (bb.) [59] | 49.83  ±1.30 | 54.43  ±2.04 | 56.84  ±2.54 | 62.22  ±0.98 | 65.08  ±5.78 | 68.32  ±1.77 | 74.40  ±1.72
SOLT-GNN [28] | 50.06  ±0.75 | 69.36  ±0.87 | 70.88  ±1.67 | 59.61  ±3.40 | 69.38  ±1.23 | 73.51  ±1.14 | 75.86  ±1.12
TopoImb [68] | 50.88  ±2.36 | 54.60  ±1.03 | 59.45  ±4.27 | 65.25  ±2.43 | 68.10  ±0.87 | 71.54  ±0.75 | 76.54  ±0.54
Imbalance Ratio: High
GIN (bb.) [59] | 50.20  ±0.69 | 53.65  ±3.89 | 55.82  ±1.76 | 61.43  ±2.36 | 62.60  ±3.82 | 67.41  ±2.23 | 74.99  ±0.95
SOLT-GNN [28] | 48.02  ±1.77 | 67.98  ±2.19 | 71.07  ±2.22 | 60.75  ±6.03 | 65.03  ±4.12 | 60.24  ±2.11 | 73.58  ±2.12
TopoImb [68] | 52.07  ±0.96 | 56.84  ±0.41 | 55.47  ±5.17 | 66.48  ±1.89 | 66.75  ±0.91 | 69.14  ±4.83 | 76.10  ±0.32

Table D.23: Micro-F1 score (% ± standard deviation) of graph classification on
manipulated topology-imbalanced graph datasets with changing imbalance levels
over 10 runs. “—” denotes out of memory or time limit. The best results are
shown in bold.

Algorithm | PTC-MR | FRANKENSTEIN | PROTEINS | D&D | IMDB-B | REDDIT-B | COLLAB
---|---|---|---|---|---|---|---
Imbalance Ratio: Low
GIN (bb.) [59] | 48.26  ±3.11 | 54.63  ±0.98 | 59.67  ±1.87 | 63.39  ±0.84 | 65.67  ±5.40 | 66.14  ±1.90 | 58.45  ±1.80
SOLT-GNN [28] | 43.63  ±1.91 | 58.54  ±1.50 | 64.60  ±4.66 | 62.34  ±0.66 | 63.66  ±5.94 | 49.17  ±6.76 | 59.76  ±1.81
TopoImb [68] | 48.87  ±2.90 | 53.07  ±0.49 | 59.94  ±4.32 | 64.97  ±1.65 | 65.71  ±2.62 | 69.15  ±3.83 | 60.91  ±2.15
Imbalance Ratio: Mid
GIN (bb.) [59] | 38.58  ±5.97 | 50.50  ±5.43 | 56.46  ±2.90 | 60.89  ±1.84 | 63.28  ±9.06 | 67.20  ±2.32 | 63.79  ±2.55
SOLT-GNN [28] | 43.20  ±5.36 | 68.52  ±1.49 | 70.58  ±2.03 | 58.67  ±4.91 | 68.73  ±1.97 | 73.24  ±1.40 | 66.96  ±1.86
TopoImb [68] | 49.17  ±0.95 | 54.25  ±0.91 | 59.03  ±4.35 | 64.65  ±1.76 | 67.98  ±0.95 | 71.52  ±0.75 | 66.58  ±1.09
Imbalance Ratio: High
GIN (bb.) [59] | 34.56  ±6.32 | 43.71  ±10.57 | 53.48  ±2.03 | 57.98  ±5.51 | 59.75  ±6.69 | 66.20  ±2.77 | 64.92  ±2.18
SOLT-GNN [28] | 40.70  ±3.27 | 67.54  ±2.28 | 70.70  ±2.20 | 58.50  ±10.48 | 64.53  ±4.68 | 54.80  ±3.23 | 64.68  ±2.81
TopoImb [68] | 51.65  ±1.07 | 56.18  ±0.53 | 44.79  ±14.19 | 63.97  ±2.78 | 66.67  ±0.91 | 68.41  ±5.34 | 65.65  ±0.63

Table D.24: AUC-ROC score (% ± standard deviation) of graph classification on
manipulated topology-imbalanced graph datasets with changing imbalance levels
over 10 runs. “—” denotes out of memory or time limit. The best results are
shown in bold.

Algorithm | PTC-MR | FRANKENSTEIN | PROTEINS | D&D | IMDB-B | REDDIT-B | COLLAB
---|---|---|---|---|---|---|---
Imbalance Ratio: Low
GIN (bb.) [59] | 51.36  ±2.71 | 57.38  ±1.46 | 60.17  ±2.84 | 66.09  ±0.71 | 71.34  ±4.89 | 78.51  ±9.44 | 77.46  ±2.90
SOLT-GNN [28] | 45.70  ±3.17 | 72.90  ±0.24 | 70.79  ±7.53 | 68.55  ±0.93 | 71.29  ±6.08 | 48.18  ±7.14 | 82.66  ±1.17
TopoImb [68] | 49.33  ±1.90 | 55.80  ±0.30 | 71.26  ±3.18 | 73.92  ±3.23 | 72.37  ±2.68 | 65.86  ±4.55 | 82.06  ±1.77
Imbalance Ratio: Mid
GIN (bb.) [59] | 48.84  ±2.20 | 54.01  ±8.26 | 53.62  ±7.67 | 67.45  ±0.86 | 68.30  ±6.16 | 78.44  ±2.37 | 86.00  ±1.23
SOLT-GNN [28] | 50.40  ±2.91 | 75.83  ±0.29 | 76.11  ±2.55 | 68.57  ±2.72 | 76.53  ±1.52 | 76.14  ±4.50 | 87.51  ±0.66
TopoImb [68] | 52.09  ±1.56 | 55.67  ±1.09 | 63.96  ±8.30 | 72.48  ±2.37 | 73.33  ±2.00 | 74.96  ±1.51 | 88.27  ±0.10
Imbalance Ratio: High
GIN (bb.) [59] | 49.85  ±1.83 | 56.40  ±9.37 | 52.96  ±7.75 | 70.66  ±0.82 | 69.92  ±3.25 | 75.86  ±5.42 | 85.97  ±0.28
SOLT-GNN [28] | 47.82  ±3.75 | 73.62  ±1.58 | 76.43  ±2.46 | 73.57  ±5.28 | 70.85  ±5.29 | 43.84  ±5.55 | 85.61  ±1.65
TopoImb [68] | 52.26  ±1.24 | 58.29  ±0.54 | 61.66  ±10.19 | 73.84  ±1.92 | 72.55  ±1.25 | 69.04  ±9.48 | 87.96  ±0.71

Table D.25: Accuracy score (% ± standard deviation) of graph classification on
manipulated topology-imbalanced graph datasets with changing imbalance levels
over 10 runs. “—” denotes out of memory or time limit. The best results are
shown in bold.

Algorithm | PTC-MR | FRANKENSTEIN | PROTEINS | D&D | IMDB-B | REDDIT-B | COLLAB
---|---|---|---|---|---|---|---
Imbalance Ratio: Low
GCN (bb.) [21] | 51.59  ±7.07 | 50.53  ±0.87 | 65.33  ±1.85 | 64.82  ±0.75 | 69.15  ±1.44 | 53.44  ±1.78 | 64.29  ±1.42
SOLT-GNN [28] | 51.45  ±3.13 | 59.25  ±0.91 | 65.24  ±4.77 | 65.69  ±2.36 | 68.23  ±2.48 | 37.58  ±3.04 | 63.82  ±2.64
TopoImb [68] | 46.74  ±1.57 | 54.36  ±0.48 | 59.73  ±5.13 | 56.18  ±2.10 | 68.20  ±0.70 | 56.94  ±3.23 | 60.47  ±0.91
Imbalance Ratio: Mid
GCN (bb.) [21] | 50.00  ±5.87 | 50.10  ±2.55 | 64.32  ±2.81 | 63.99  ±2.16 | 67.95  ±2.82 | 67.96  ±0.89 | 67.64  ±2.04
SOLT-GNN [28] | 56.23  ±0.84 | 66.42  ±1.37 | 68.91  ±1.89 | 62.78  ±1.33 | 70.25  ±1.15 | 61.95  ±5.55 | 66.94  ±3.67
TopoImb [68] | 54.13  ±4.62 | 55.38  ±0.90 | 49.72  ±13.46 | 64.73  ±7.09 | 68.75  ±0.76 | 69.12  ±0.52 | 66.48  ±1.03
Imbalance Ratio: High
GCN (bb.) [21] | 49.93  ±5.90 | 51.12  ±1.01 | 58.02  ±5.02 | 60.98  ±6.71 | 64.88  ±2.02 | 66.38  ±0.46 | 68.99  ±1.36
SOLT-GNN [28] | 54.78  ±6.03 | 68.26  ±0.28 | 67.38  ±2.89 | 63.21  ±3.40 | 69.80  ±2.07 | 67.05  ±2.54 | 65.57  ±5.59
TopoImb [68] | 51.81  ±1.26 | 55.20  ±0.59 | 54.31  ±13.19 | 69.66  ±1.92 | 66.60  ±0.91 | 69.09  ±1.00 | 67.74  ±0.63

Table D.26: Balanced Accuracy score (% ± standard deviation) of graph
classification on manipulated topology-imbalanced graph datasets with changing
imbalance levels over 10 runs. “—” denotes out of memory or time limit. The
best results are shown in bold.

Algorithm | PTC-MR | FRANKENSTEIN | PROTEINS | D&D | IMDB-B | REDDIT-B | COLLAB
---|---|---|---|---|---|---|---
Imbalance Ratio: Low
GCN (bb.) [21] | 50.47  ±0.75 | 52.46  ±0.50 | 61.92  ±2.38 | 63.13  ±0.43 | 69.15  ±1.44 | 53.44  ±1.78 | 70.14  ±1.68
SOLT-GNN [28] | 48.24  ±1.20 | 63.10  ±0.74 | 61.76  ±3.57 | 63.81  ±1.86 | 68.23  ±2.48 | 37.58  ±3.04 | 69.49  ±0.19
TopoImb [68] | 50.43  ±0.87 | 55.53  ±0.61 | 62.18  ±2.05 | 57.64  ±0.94 | 68.20  ±0.70 | 56.94  ±3.23 | 69.51  ±0.91
Imbalance Ratio: Mid
GCN (bb.) [21] | 49.74  ±2.52 | 50.83  ±0.66 | 61.89  ±1.10 | 58.27  ±4.65 | 67.95  ±2.82 | 67.96  ±0.89 | 76.18  ±0.89
SOLT-GNN [28] | 51.13  ±0.79 | 66.62  ±1.36 | 67.58  ±2.10 | 59.12  ±2.47 | 70.25  ±1.15 | 61.95  ±5.55 | 74.88  ±1.59
TopoImb [68] | 54.34  ±3.22 | 54.62  ±1.00 | 54.47  ±6.12 | 64.63  ±3.42 | 68.75  ±0.76 | 69.12  ±0.52 | 74.87  ±0.87
Imbalance Ratio: High
GCN (bb.) [21] | 49.96  ±0.54 | 52.43  ±1.04 | 52.66  ±2.17 | 57.58  ±4.32 | 64.88  ±2.02 | 66.38  ±0.46 | 66.80  ±1.08
SOLT-GNN [28] | 51.11  ±1.15 | 68.06  ±0.41 | 66.34  ±2.08 | 60.94  ±1.68 | 69.80  ±2.07 | 67.05  ±2.54 | 74.16  ±2.63
TopoImb [68] | 52.12  ±0.78 | 55.50  ±1.13 | 55.34  ±5.76 | 66.63  ±4.54 | 66.60  ±0.91 | 69.09  ±1.00 | 75.02  ±0.79

Table D.27: Macro-F1 score (% ± standard deviation) of graph classification on
manipulated topology-imbalanced graph datasets with changing imbalance levels
over 10 runs. “—” denotes out of memory or time limit. The best results are
shown in bold.

Algorithm | PTC-MR | FRANKENSTEIN | PROTEINS | D&D | IMDB-B | REDDIT-B | COLLAB
---|---|---|---|---|---|---|---
Imbalance Ratio: Low
GCN (bb.) [21] | 36.72  ±5.58 | 50.16  ±1.26 | 62.08  ±2.40 | 63.09  ±0.46 | 69.02  ±1.52 | 49.68  ±8.19 | 61.44  ±1.38
SOLT-GNN [28] | 45.00  ±3.14 | 57.49  ±1.18 | 61.41  ±4.07 | 63.82  ±2.01 | 67.88  ±2.35 | 35.00  ±2.77 | 61.07  ±1.80
TopoImb [68] | 44.72  ±2.61 | 54.31  ±0.49 | 58.67  ±6.03 | 55.77  ±1.91 | 67.78  ±1.00 | 56.09  ±3.68 | 58.79  ±1.01
Imbalance Ratio: Mid
GCN (bb.) [21] | 40.94  ±5.67 | 48.11  ±3.33 | 61.59  ±1.64 | 54.22  ±8.96 | 67.80  ±2.84 | 67.18  ±1.39 | 65.45  ±1.75
SOLT-GNN [28] | 45.63  ±4.84 | 66.16  ±1.30 | 67.16  ±2.03 | 58.14  ±3.23 | 70.05  ±1.19 | 57.57  ±8.59 | 64.70  ±3.08
TopoImb [68] | 51.99  ±3.88 | 54.34  ±0.88 | 40.81  ±15.22 | 62.10  ±6.59 | 68.64  ±0.77 | 69.10  ±0.49 | 64.49  ±0.93
Imbalance Ratio: High
GCN (bb.) [21] | 39.32  ±7.82 | 50.84  ±1.33 | 51.29  ±1.10 | 52.46  ±8.79 | 63.65  ±3.15 | 65.91  ±0.31 | 66.80  ±1.08
SOLT-GNN [28] | 39.57  ±6.16 | 67.89  ±0.33 | 65.88  ±2.46 | 60.32  ±2.31 | 69.54  ±2.16 | 65.40  ±3.77 | 63.70  ±4.83
TopoImb [68] | 51.43  ±0.98 | 54.99  ±0.81 | 44.51  ±14.79 | 65.66  ±5.28 | 66.54  ±0.89 | 68.76  ±1.17 | 65.56  ±0.52

Table D.28: AUC-ROC score (% ± standard deviation) of graph classification on
manipulated topology-imbalanced graph datasets with changing imbalance levels
over 10 runs. “—” denotes out of memory or time limit. The best results are
shown in bold.

Algorithm | PTC-MR | FRANKENSTEIN | PROTEINS | D&D | IMDB-B | REDDIT-B | COLLAB
---|---|---|---|---|---|---|---
Imbalance Ratio: Low
GCN (bb.) [21] | 50.81  ±2.98 | 53.52  ±0.69 | 62.80  ±5.19 | 64.25  ±0.94 | 74.69  ±1.04 | 50.48  ±13.45 | 81.81  ±0.88
SOLT-GNN [28] | 46.36  ±0.64 | 73.17  ±0.36 | 59.26  ±6.01 | 65.61  ±1.44 | 74.16  ±1.36 | 32.50  ±5.56 | 80.89  ±1.27
TopoImb [68] | 52.94  ±0.50 | 56.71  ±0.57 | 67.71  ±4.70 | 60.66  ±1.62 | 74.55  ±1.80 | 63.78  ±2.65 | 82.67  ±0.42
Imbalance Ratio: Mid
GCN (bb.) [21] | 50.03  ±4.80 | 51.66  ±0.64 | 62.02  ±1.93 | 61.45  ±4.93 | 74.23  ±3.12 | 74.51  ±2.91 | 87.46  ±0.79
SOLT-GNN [28] | 52.54  ±0.92 | 72.48  ±1.32 | 71.33  ±2.35 | 59.75  ±4.06 | 78.21  ±2.21 | 66.93  ±6.74 | 86.46  ±0.45
TopoImb [68] | 57.29  ±2.45 | 56.98  ±1.58 | 65.74  ±3.16 | 74.47  ±2.44 | 74.30  ±0.66 | 77.25  ±0.41 | 86.74  ±0.85
Imbalance Ratio: High
GCN (bb.) [21] | 51.12  ±1.94 | 52.85  ±2.56 | 47.22  ±5.45 | 65.50  ±6.38 | 68.31  ±3.07 | 73.41  ±0.82 | 87.56  ±0.44
SOLT-GNN [28] | 49.47  ±4.36 | 73.27  ±0.46 | 69.84  ±3.01 | 64.79  ±0.57 | 78.04  ±1.14 | 72.92  ±1.77 | 86.77  ±1.65
TopoImb [68] | 53.65  ±2.72 | 57.66  ±0.95 | 63.26  ±12.24 | 74.37  ±3.19 | 71.84  ±1.07 | 75.52  ±1.17 | 88.42  ±0.13

####  D.2 Additional Results for Algorithm Robustness (RQ2)

#####  D.2.1 Robustness of Node-Level Class-Imbalanced Algorithms

Figure D.1: Generalizability analysis of the node-level algorithms under
different class-imbalance degrees on Cora (homophilic). Results are reported
with the algorithm performance (Accuracy) and its relative decrease (%)
compared to the class-balanced data split (the green bar). Figure D.2:
Generalizability analysis of the node-level algorithms under different class-
imbalance degrees on CiteSeer (homophilic). Results are reported with the
algorithm performance (Accuracy) and its relative decrease (%) compared to the
class-balanced data split (the green bar). Figure D.3: Generalizability
analysis of the node-level algorithms under different class-imbalance degrees
on Chameleon (heterophilic). Results are reported with the algorithm
performance (Accuracy) and its relative decrease (%) compared to the class-
balanced data split (the green bar). Figure D.4: Generalizability analysis of
the node-level algorithms under different class-imbalance degrees on Squirrel
(heterophilic). Results are reported with the algorithm performance (Accuracy)
and its relative decrease (%) compared to the class-balanced data split (the
green bar).

#####  D.2.2 Robustness of Node-Level Local Topology-Imbalanced Algorithms

Figure D.5: Robustness analysis of the node-level algorithms under different
local topology-imbalance degrees (Low, Mid, and High). Results are reported
with the algorithm performance (Accuracy) with the standard deviation error
area.

#####  D.2.3 Robustness of Node-Level Global Topology-Imbalanced Algorithms

Figure D.6: Robustness analysis of the node-level algorithms under different
global topology-imbalance degrees (Low, Mid, and High). Results are reported
with the algorithm performance (Accuracy) with the standard deviation error
area.

#####  D.2.4 Robustness of Graph-Level Topology-Imbalanced Algorithms

Figure D.7: Robustness analysis of the graph-level algorithms under different
class-imbalance degrees (Low, Mid, and High). Results are reported with the
algorithm performance (Accuracy) with the standard deviation error area.

#####  D.2.5 Robustness of Graph-Level Topology-Imbalanced Algorithms

Figure D.8: Robustness analysis of the graph-level algorithms under different
topology-imbalance degrees (Low, Mid, and High). Results are reported with the
algorithm performance (Accuracy) with the standard deviation error area.

####  D.3 Additional Results for Visualizations (RQ3)

#####  D.3.1 Visualizations of Node-Level Class-Imbalanced Algorithms

Figure D.9: Visualizations of the embedding for node-level class-imbalanced
algorithms.

#####  D.3.2 Visualizations of Node-Level Local Topology-Imbalanced Algorithms

Figure D.10: Visualizations of the embedding for node-level local topology-
imbalanced algorithms.

#####  D.3.3 Visualizations of Node-Level Global Topology-Imbalanced
Algorithms

Figure D.11: Visualizations of the embedding for node-level global topology-
imbalanced algorithms.

#####  D.3.4 Visualizations of Graph-Level Class-Imbalanced Algorithms

Figure D.12: Visualizations of the embedding for graph-level class-imbalanced
algorithms.

#####  D.3.5 Visualizations of Graph-Level Topology-Imbalanced Algorithms

Figure D.13: Visualizations of the embedding for global-level topology-
imbalanced algorithms.

####  D.4 Additional Results for Efficiency Analysis (RQ4)

#####  D.4.1 Efficiency Analysis of Node-Level Class-Imbalanced Algorithms

Figure D.14: Time and space analysis of node-level class-imbalanced IGL
algorithms on Actor. Figure D.15: Time and space analysis of node-level class-
imbalanced IGL algorithms on ogbn-arXiv.

#####  D.4.2 Efficiency Analysis of Node-Level Local Topology-Imbalanced
Algorithms

Figure D.16: Time and space analysis of node-level local topology-imbalanced
IGL algorithms on Actor. Figure D.17: Time and space analysis of node-level
local topology-imbalanced IGL algorithms on ogbn-arXiv.

#####  D.4.3 Efficiency Analysis of Node-Level Global Topology-Imbalanced
Algorithms

Figure D.18: Time and space analysis of node-level global topology-imbalanced
IGL algorithms on Actor. Figure D.19: Time and space analysis of node-level
global topology-imbalanced IGL algorithms on ogbn-arXiv.

#####  D.4.4 Efficiency Analysis of Graph-Level Class-Imbalanced Algorithms

Figure D.20: Time and space analysis of graph-level class-imbalanced IGL
algorithms on COLLAB.

#####  D.4.5 Efficiency Analysis of Graph-Level Topology-Imbalanced Algorithms

Figure D.21: Time and space analysis of graph-level topology-imbalanced IGL
algorithms on COLLAB.

###  Appendix E Package and Reproducibility

$\bm{\rho}$

Figure E.1: The package structure of IGL-Bench, which mainly consists of four
modules. Figure E.2: The IGL-Bench package.

Package. We established and released a comprehensive Imbalanced Graph Learning
Benchmark (IGL-Bench) package, which serves as the first open-
sourced555https://github.com/RingBDStack/IGL-Bench benchmark for graph-
specific imbalanced learning to the best of our knowledge. IGL-Bench
encompasses 24 state-of-the-art IGL algorithms and 16 diverse graph datasets
covering node-level and graph-level tasks, addressing class- and topology-
imbalance issues, while also adopting consistent data processing and splitting
approaches for fair comparisons over multiple metrics with different focus.

As shown in Figure E.1, the IGL-Bench package is mainly composed of four
modules. ❶ The Imbalance Manipulator module performs different types of
imbalance manipulations for the imbalance ratio on the built-in 16 node-level
datasets, graph-level datasets, or user-defined datasets according to user
configurations. ❷ The IGL Algorithms module has 24 state-of-the-art algorithms
built-in and also supports calling user-defined IGL algorithms. ❸ The GNN
Backbones module supports a variety of mainstream GNNs and also allows for
user-defined GNNs. ❹ The Package Utils module offers a variety of utility
tools, enhancing the usability and benchmarking efficiency of the package.

Documentation and Uses. We have made a concerted effort to provide users with
comprehensive documentation to ensure the seamless use of the package.
Additionally, we have included necessary comments to enhance code readability.
We supply the required configuration files to reproduce the experimental
results, which also serve as examples of how to use the package effectively.

License. Our package (codes and datasets) is licensed under the MIT License.
This license permits users to freely use, copy, modify, merge, publish,
distribute, sublicense, and sell copies of the software, provided that the
original copyright notice and permission notice are included in all copies or
substantial portions of the software. The MIT License is widely accepted for
its simplicity and permissive terms, ensuring ease of use and contribution to
the codes and datasets. We bear all responsibility in case of violation of
rights, etc, and confirmation of the data license.

Code Maintenance. We are committed to continuously updating our code and
actively addressing users’ issues and feedback. Additionally, we warmly
welcome community contributions to enhance our library and benchmark
algorithms. Nonetheless, we will enforce strict version control measures to
ensure reproducibility throughout the maintenance process.

###  Appendix F Further Discussions

####  F.1 Related Works

To the best of our knowledge, there exists no established benchmark
specifically dedicated to evaluating imbalanced learning on graphs. Our IGL-
Bench represents the foundational effort in this domain, encompassing both
node-level and graph-level challenges related to class- and topology-
imbalance. This section compares and contextualizes our contributions within
the broader landscape of imbalanced graph learning. We position our work in
relation to notable surveys in the field.

[27] comprehensively reviews the landscape of imbalanced learning on graphs,
outlining key terminologies and taxonomies related to problem types and
solution strategies. It establishes a foundational understanding crucial for
addressing skewed data distributions in graph-based tasks.

Focused on the challenges of GNNs in practical applications, [18] addresses
issues such as imbalance in data distribution and the robustness against
noise, privacy concerns, and out-of-distribution scenarios. It highlights
solutions that enhance the reliability of GNNs in real-world settings.

[32] specifically explores class-imbalanced learning on graphs, emphasizing
the integration of graph representation learning with imbalanced learning
techniques. It provides a taxonomy of existing approaches and outlines future
directions in the evolving field of graph class-imbalanced learning.

In contrast to these surveys, our IGL-Bench offers a practical benchmarking
package tailored explicitly for imbalanced graph learning. By systematically
evaluating the performance of algorithms across various imbalance types, IGL-
Bench provides a standardized package for assessing the efficacy and
robustness of existing and future methods in this emerging field. While
existing surveys establish the theoretical underpinnings and methodological
approaches in imbalanced learning on graphs, IGL-Bench offers a concrete tool
for empirical validation and comparison. This practical focus enables
researchers and practitioners to not only understand the theoretical aspects
but also to apply and benchmark algorithms effectively across diverse real-
world graph datasets.

In summary, our work fills a critical gap by introducing IGL-Bench as the
first benchmarking suite tailored for imbalanced graph learning, thereby
advancing the state-of-the-art in the field and fostering deeper insights into
the challenges and opportunities of imbalanced graph data analysis.

####  F.2 Limitations

IGL-Bench has some limitations that we aim to address in future work.

❶ We hope to include a broader range of datasets to evaluate algorithms in
different scenarios. Our current datasets are predominantly homogeneous
graphs, which do not fully capture the diversity and complexity of real-world
networks. Many IGL methods struggle with complex graph types, such as
heterogeneous graphs with multiple types of nodes and edges. Including such
datasets would provide a more robust evaluation of these algorithms and
highlight their strengths and weaknesses.

❷ We hope to implement more IGL algorithms for various tasks, such as few-shot
classification, dynamic graph learning, and anomaly detection, etc Our current
benchmark is limited to a specific set of tasks, which might not reflect the
full potential and versatility of IGL methods. By expanding the range of
tasks, we can gain a deeper understanding of the progress in the field and
provide insights into how different algorithms perform across diverse
applications.

❸ Due to resource constraints and the availability of implementations, we
could not include some of the latest state-of-the-art IGL algorithms in our
benchmark. This might impact the comprehensiveness of our evaluation, as some
promising methods are not represented. We aim to address this by continuously
updating our package and incorporating these algorithms as they become
available.

❹ Our current evaluation framework primarily focuses on the performance
metrics of the algorithms. However, practical aspects such as scalability,
computational efficiency, and memory usage are also crucial for real-world
applications. We plan to include these factors in future evaluations to
provide a more holistic view of each algorithm’s practicality and efficiency.

We will continuously update our repository to keep track of the latest
advances in the field. We are also open to any suggestions and contributions
that will improve the usability and effectiveness of our benchmark, ensuring
it remains a valuable resource for the IGL research community.

####  F.3 Dataset Privacy and Ethics

We ensured all datasets were sourced from publicly available repositories with
explicit research permissions. For user-generated or social platform data, we
rely on terms including research consent. We anonymized Personally
Identifiable Information (PII) and screened for offensive content, though
complete risk elimination remains challenging. Users are urged to use datasets
responsibly, mindful of ethical implications.