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Benchmark Results and Experimental Setup

Below are the key tables summarizing the datasets we used and the link‑prediction results obtained with various methods, followed by detailed information about our software setup, installation steps, datasets, and how to reproduce our experiments.

Dataset Statistics

Type Dataset # Nodes # Edges # Features # Classes
Homophilous Cora 2,708 10,556 1,433 7
Homophilous CiteSeer 3,327 9,104 3,703 6
Homophilous PubMed 19,717 88,648 500 3
Homophilous FB Page-Page 22,470 171,002 31 4
Homophilous Coauthor-Physics 34,493 495,924 8,415 5
Homophilous Facebook 4,039 88,234 1,283 193
Homophilous DBLP 17,716 105,734 1,639 4
Heterophilous Roman-Empire 22,662 32,927 300 18
Heterophilous Amazon-Ratings 24,492 93,050 300 5
Heterophilous Questions 48,921 153,540 301 2
Heterophilous Chameleon 2,277 36,101 2,325 5
Heterophilous Actor 7,600 33,544 931 5
Heterophilous Crocodile 1,118 15,620 1,438 3

Link‑Prediction Results on Homophilous Graphs

Method Cora (HR@100) Citeseer (HR@100) Pubmed (HR@100) FB Page‑Page (MRR) Facebook (HR@100) Coauthor‑Physics (MRR) DBLP (HR@10)
CN 33.92 29.79 23.13 17.85 84.38 18.57 32.8
AA 39.85 35.19 27.38 22.60 88.14 22.31 21.13
RA 41.07 33.56 27.03 20.54 92.58 21.46 22.47
GCN 66.79±1.65 67.08±2.94 53.02±1.39 11.26±1.6 92.85±0.61 14.68±3.40 33.30±4.74
SAGE 55.02±4.03 57.01±3.57 44.29±1.44 10.44±2.48 68.50±8.6 13.07±1.02 31.06±5.98
GAE 89.01±1.32 91.78±0.94 78.81±1.64 12.93±0.66 92.68±2.58 15.83±1.67 41.38±3.72
Neo‑GNN 80.42±1.34 84.67±1.42 73.93±1.19 12.43±0.22 91.24±0.77 20.94±3.94 50.05±3.40
BUDDY 88.00±0.44 92.93±0.27 74.10±0.78 16.94±1.37 87.56±1.43 14.26±1.82 31.74±6.09
NCN 89.05±0.96 91.56±1.43 79.05±1.16 9.16±1.96 93.67±0.82 29.05±3.48 51.26±3.26
NCNC 89.65±1.36 93.47±0.95 81.29±0.85 14.03±7.88 92.78±2.00 20.99±5.09 42.82±4.12
NCN + Class label 95.71±1.10 96.96±0.37 90.81±1.13 11.27±4.62 93.69±0.62 27.04±3.93 51.75±2.55
CGLE(NCN) (True CL) 95.77±0.62 97.27±0.74 90.49±0.54 12.06±5.57 93.75±0.79 26.97±4.32 51.33±2.00
NCNC + Class label 88.63±1.72 92.46±1.05 82.02±1.51 12.72±8.41 92.95±0.62 21.48±6.47 42.54±4.28
CGLE(NCNC) (True CL) 91.41±1.36 92.31±0.14 82.06±0.13 23.84±6.15 93.92±0.56 21.24±3.06 49.00±3.10
CGLE(NCN)‑kmeans 94.27±0.94 95.89±1.84 90.44±0.83 7.84±1.28 93.99±0.59 27.29±3.47 52.86±1.48
CGLE(NCNC)‑kmeans 94.80±0.96 96.90±1.12 91.65±0.60 16.32±5.70 93.61±0.90 24.94±4.42 48.88±3.21

Link‑Prediction Results on Heterophilous Graphs

Method Roman Empire (MRR) Amazon‑ratings (MRR) Questions (HR@100) Chameleon (MRR) Actor (HR@100)
NCN 54.29±0.86 55.90±7.51 62.25±1.75 76.79±1.33 53.18±1.65
NCNC 28.23±12.51 72.63±6.69 62.93±1.73 74.75±8.37 50.77±3.07
NCN + Class 52.32±1.96 59.88±8.72 63.89±1.40 77.09±2.92 51.01±2.35
NCNC + Class 32.35±11.88 67.56±3.17 63.89±1.40 73.68±7.78 51.48±1.19
CGLE(NCN) (True CL) 54.01±0.71 64.68±8.25 63.02±1.55 81.15±3.09 53.37±1.71
CGLE(NCNC) (True CL) 52.23±2.31 70.62±5.96 63.44±1.57 77.88±8.29 51.07±4.31
CGLE‑kmeans(NCN) 53.19±1.44 64.03±6.87 61.33±2.98 77.32±4.19 54.82±1.57
CGLE‑kmeans(NCNC) 53.82±2.57 73.67±5.11 63.95±2.82 77.87±5.45 51.42±3.87
Metric Dataset NCNC k=2 k=5 k=10 k=15 k=20
HR@100 Cora 89.65±1.36 94.80±0.96 94.54±0.78 94.58±0.95 94.39±1.36 94.31±1.35
HR@100 Citeseer 93.47±0.95 96.55±1.65 96.66±1.52 96.22±2.49 96.30±2.44 96.90±1.12
HR@100 Pubmed 81.29±0.85 91.52±0.37 91.30±0.70 91.36±0.62 91.23±0.26 91.65±0.60
HR@100 Facebook 92.78±2.00 93.61±0.90 93.36±1.74 93.44±1.15 93.38±1.78 93.54±1.43
MRR FB Page‑Page 14.03±7.88 12.97±4.48 16.32±5.70 11.58±3.51 13.07±2.65 15.32±5.22
MRR Coauthor‑Physics 20.99±5.09 23.81±2.31 24.94±4.42 24.28±2.51 23.67±3.26 22.47±1.43
HR@10 DBLP 42.82±4.12 48.88±3.21 49.14±2.99 49.08±4.50 48.11±3.99 46.96±5.56
MRR Roman Empire 28.23±12.51 52.93±1.95 53.82±2.57 53.50±2.19 53.25±2.48 53.35±1.74
MRR Amazon‑ratings 72.73±6.69 73.67±5.11 69.96±6.86 72.74±4.56 69.23±8.47 68.50±7.54
MRR Chameleon 74.75±8.37 77.61±11.03 77.11±6.37 77.28±7.44 77.87±5.45 75.97±8.60
HR@100 Questions 62.93±1.73 63.00±2.43 63.21±2.79 63.59±2.40 63.15±2.53 63.95±2.82
HR@100 Actor 50.77±3.07 51.15±3.65 51.42±3.87 51.39±3.39 51.72±2.62 51.09±3.69
Metric Dataset NCN k=2 k=5 k=10 k=15 k=20
HR@100 Cora 89.05±0.96 94.18±1.00 94.23±0.92 94.21±0.94 94.27±0.94 94.16±0.90
HR@100 Citeseer 91.56±1.43 95.45±2.71 95.80±2.22 95.56±2.22 95.67±2.79 95.89±1.84
HR@100 Pubmed 79.05±1.16 90.04±0.78 90.39±0.81 90.38±0.86 90.44±0.83 90.38±0.82
HR@100 Facebook 93.67±0.82 93.59±0.77 93.85±0.50 93.74±0.67 93.99±0.59 93.55±0.63
MRR FB Page‑Page 9.16±1.96 7.60±2.03 7.37±1.84 7.26±1.24 7.76±1.21 7.84±1.28
MRR Coauthor‑Physics 29.05±3.48 26.08±3.19 24.91±3.45 26.89±2.68 27.29±3.47 26.48±0.32
HR@10 DBLP 51.26±3.26 51.53±2.17 52.86±1.48 50.99±2.84 51.49±2.10 51.11±2.30
MRR Roman Empire 54.29±0.86 53.19±1.44 52.46±1.85 52.25±1.81 52.54±1.74 52.98±2.25
MRR Amazon‑ratings 55.90±7.51 61.55±5.46 60.93±4.35 61.92±6.52 60.38±7.23 64.03±6.87
MRR Chameleon 76.79±1.33 76.55±3.53 75.24±7.43 75.47±5.23 77.32±4.19 75.63±6.22
HR@100 Questions 62.25±1.75 60.57±3.42 61.33±2.98 61.83±1.03 59.70±3.39 60.88±2.46
HR@100 Actor 53.18±1.65 54.82±1.57 54.56±2.48 54.64±1.85 54.32±1.91 54.72±1.72

Latest Setup

  • Python: 3.10.14
  • PyTorch: 2.3.1 (CUDA 12.1)
  • PyTorch Geometric: 2.5.3
  • OGB: 1.3.6

Hardware: Experiments were conducted using NVIDIA A100 (80GB) and NVIDIA V100 GPUs.

Installation Guide

  1. Install PyTorch.
  2. Install PyTorch Geometric.
  3. Install OGB.

Datasets

  1. Facebook Page-Page Network: We used the dataset from Facebook Large Page-Page Network. Since not all features have the maximum dimension of 31, we concatenated them with zeros to make all node feature dimensions consistent at 31. The dataset can be found in the CGLE/datasets/fb_page directory.

  2. Other Datasets: We used datasets from PyTorch Geometric.

Getting Started

Clone the repository and navigate to the project directory:

git clone <repository_url>

Running Experiments

  • To reproduce NCNC:

    bash ncnc_run.sh

  • To reproduce NCN:

    bash ncn_run.sh

  • To reproduce NCNC ⊕ Class labels:

    bash ncnc_concat_y.sh

  • To reproduce NCN ⊕ Class labels:

    bash ncn_concat_y.sh

  • To reproduce CGLE(NCNC):

    bash cgle_ncnc.sh

  • To reproduce CGLE(NCN):

    bash cgle_ncn.sh

  • To reproduce CGLE(NCNC) with k-means:

    bash cgle_ncnc_k-means.sh

  • To reproduce CGLE(NCN) with k-means:

    bash cgle_ncn_k-means.sh

Acknowledgments

This implementation was inspired by the following repositories:

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Artefacts related to CGLE paper in ICDM 2025.

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