linkwise

Topology-Driven Edge Predictions with Graph Machine Learning for Optical Network Growth:

Graph representation learning on real-world optical core networks outperforms edge prediction heuristics by 10 times, achieving up to 93.4% accuracy on BT(UK), COST(EU), and CORONET(USA) by learning from 10% training data.

Dataset

• COST266: A European network topology with 37 nodes and 57 links. Nodes represent cities, and edges represent fiber links between cities.
• CORONET CONUS-60: A US backbone network topology with 60 nodes and 75 links.
• BT: UK's core backbone optical network with 106 nodes and 180 edges

Linkwise: Node2Vec and Logistic Regression

We implement a link prediction pipeline using graph embeddings and logistic regression on network topologies - BT, COST and CORONET.

Model Evaluation using Test Accuracy

Comparison with Heuristics

Topology	Baseline (t = 0.5)	Accuracy (t = 0.5)	Baseline (t = 0.1)	Accuracy (t = 0.1)
COST	0.0714 (Pagerank)	0.94 ± 0.01	0.0784 (Adamic Adar)	0.88 ± 0.04
BT	0.1222 (Adamic Adar)	0.93 ± 0.01	0.0432 (Jaccard)	0.93 ± 0.01
CORONET	0.0256 (Jaccard)	0.88 ± 0.05	0.0423 (Random)	0.89 ± 0.00

Methodology

The pipeline follows these key steps:

• Construct the graph and compute geographical distance features between nodes.
• Generate Node2Vec embeddings for the nodes.
• Extract positive (connected) and negative (unconnected) edges from the graph.
• Split the edges into training and test sets.
• Train a logistic regression classifier with distance and embedding dot product features.
• Evaluate classifier performance using AUC-ROC, precision, recall etc.
• Visualize results using plots.

Key Functions:

• setup_cost266_graph(): Creates the COST266 graph.
• setup_coronet_conus60_graph(): Creates the CORONET CONUS-60 graph.
• generate_node2vec_embeddings(): Generates node embeddings.
• train_classifier(): Trains the classifier.
• evaluate_classifier(): Evaluates classifier performance.
• visualise_metrics(): Visualizes results.
• run_pipeline(): Runs the pipeline end-to-end.
• main() function runs the pipeline for different test set sizes.

Heuristics

• Link prediction methods:
• • Jaccard Coefficient
• • Adamic Adar Index
• • Preferential Attachment
• • Resource Allocation Index
• • Common Neighbors
• • Triadic Closure
• • Random
• • Katz Index
• • Rooted PageRank
• Functions to run predictions and evaluate accuracy
• Sample runs on the graphs with different random seeds
• seeds_to_test - Random seeds
• percentages_to_test - Percentage of edges to remove
• Output: accuracy of different prediction methods when a percentage of edges are removed from the graphs.

Python Packages (Python 3.10.12)

• numpy
• pandas
• folium
• networkx
• node2vec
• scikit-learn
• matplotlib
• seaborn
• torch

Data Sources and Formats:

• COST has been taken from SNDLib http://sndlib.zib.de/home.action
• CORONET has been taken from https://github.com/XuYZh/Network-Pruning-and-Growth---Probabilistic-Optimization
• Raw dataset files have been added for users in case they need them.
• We process these topologies as graphs and manually hardcoded them into our code to be available in the Networkx format suitable for our analysis
• We also have processed and saved Networkx into multiple formats for the user.

Please Note:

• Data about BT's infrastructure is not available due to privacy concerns. Users can utilise the COST or CORONET topologies provided in the code for analysis.
• Random seeds can generate different results at each run; irrespective of the minor changes, the performance gains for our model compared to heuristics remain 10x.

References

• S. Orlowski, R. Wessäly, M. Pióro, A. Tomaszewski, "Sndlib 1.0—Survivable Network Design Library," Networks, vol. 55, no. 3, pp. 276--286, 2010.
• Y.-Z. Xu, D. Saad, "Network Pruning and Growth: Probabilistic Optimization," Physical Review Research, vol. 5, no. 3, 033087, 2023.
• A. Grover, J. Leskovec, "node2vec: Scalable Feature Learning for Networks," in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2016, pp. 855--864.
• R. Matzner, D. Semrau, R. Luo, G. Zervas, P. Bayvel, "Making Intelligent Topology Design Choices: Understanding Structural & Physical Property Performance Implications in Optical Networks," Journal of Optical Communications and Networking, vol. 13, no. 8, pp. D53--D67, 2021.
• M. Zhang, "Graph Neural Networks: Link Prediction," in Graph Neural Networks: Foundations, Frontiers, and Applications, L. Wu, P. Cui, J. Pei, L. Zhao, Eds. Springer Singapore, 2022, pp. 195--223.
• P. Wright, R. Davey, A. Lord, "Cost Model Comparison of ZR/ZR+ Modules Against Traditional WDM Transponders for 400G IP/WDM Core Networks," in 2020 European Conference on Optical Communications (ECOC), IEEE, 2020, pp. 1--4.