Graph Topology Utilization in Optical Networks

• Graph topology utilization is the strategic application of structural, spatial, and spectral metrics to analyze network graphs in optical benchmarking and design.
• It combines diverse real-world and synthetic datasets to capture key characteristics such as sparsity, resilience, and network efficiency.
• Objective benchmarking is achieved through unsupervised clustering and statistical correlation, guiding robust and reproducible optical network research.

Graph topology utilization refers to the rigorous characterization, measurement, and application of the structural, spatial, and spectral properties of network graphs within the context of optical core network benchmarking and design. The "Topology Bench" framework exemplifies this by establishing a comprehensive dataset, a systematic metric suite, and an objective methodology for analysis and representative selection of both real and synthetic network topologies, addressing prior limitations in scale, diversity, and reproducibility.

1. Multidimensional Graph Metric Analysis

Topology Bench employs a comprehensive suite of graph-theoretical metrics—structural, spatial, and spectral—to profile and compare network topologies:

• Structural metrics include node degree ($d(v)$), average degree ($\bar{d} = 2m/n$), network density ($ND = 2m/(n(n-1))$), diameter ($D$), average shortest path length ($L$), clustering coefficient ($C(v)$), maximum node/edge betweenness, and global efficiency ($E_\text{glob}$).
• Spatial metrics account for real-world edge distances via fiber length estimation procedures that utilize the Haversine formula and empirically derived multipliers for different link length regimes, resulting in per-path and per-edge physical distance statistics.
• Spectral metrics include the spectral radius ($\rho(A)$), algebraic connectivity ($\lambda_{AC}$, the second smallest Laplacian eigenvalue), and weighted spectral distribution ($WSD(G)$), which summarizes the eigenvalue spread of the normalized Laplacian matrix.

These metrics are explicitly formulated, e.g.: $d(v) = \sum_{u \in V}A(v, u)$

$ND = \frac{2m}{n(n-1)}$

$$E_\text{glob} = \frac{1}{n(n-1)} \sum_{u \neq v} \frac{1}{d(u,v)}$$

where $A$ is the adjacency matrix and $d(u,v)$ denotes shortest path length.

This multidimensional approach enables nuanced clustering and benchmarking across properties such as sparsity, resilience, efficiency, and physical embedding.

2. Dataset Composition and Diversity

Topology Bench compiles two unprecedentedly large and heterogeneous collections:

• Real-World Topologies: 105 georeferenced core optical network graphs, spanning national, continental, and global scales, collected from SNDLib, TopoHub, legacy sources, and reconstructed diagrams, with consistent CSV formatting including explicit geographic coordinates and planarity/biconnectivity annotations. 93% are planar, with 52 strictly biconnected and 53 containing bridges (single points of failure).
• Synthetic Topologies: 270,900 SNR-BA synthetic graphs (Stochastic Nearest-neighbor Randomized Barabási-Albert), with parameter sweeps across node count ($n$), network density, and geographic scale, validated for distributional similarity on key metrics (diameter, spectral, and fiber length) via Kolmogorov-Smirnov testing.

This dataset represents a 61.5% increase in georeferenced real-world topologies and, for the first time, provides open, large-scale synthetic optical network test cases for unbiased benchmarking.

3. Objective Benchmarking and Topology Selection

The framework replaces ad hoc or subjective topology selection with a systematic, repeatable procedure:

• Quantitative Topology Profiling: All networks are exhaustively characterized using the metric suite, enabling inter- and intra-dataset diversity analysis.
• Unsupervised Machine Learning Clustering: K-means is applied in a metric space defined by nine optimal features (after PCA and SVM filtering): number of nodes, density, maximum node/edge betweenness, average shortest path, average degree, clustering coefficient, algebraic connectivity, and normalized spectral radius.
• Cluster-Guided Selection: For future benchmarking, selecting at least one topology per cluster ensures coverage of the full operational diversity observed in practice, mitigating sampling bias and improving generalizability and fairness in comparative studies.
• Synthetic Topology Augmentation: Synthetic graphs, mapped by metrics to fill voids in the real-world cluster space, enable systematic stress-testing and scaling studies beyond observed deployments.

4. Statistical and Correlation Insights

Detailed statistical and correlation analyses provide key scientific findings:

• Real core optical networks are predominantly sparse, low-degree, and planar, with most exhibiting zero clustering (indicative of grid, tree, or hierarchical structures).
• Correlation matrices (using Pearson coefficients) reveal:
  • High positive correlation between algebraic connectivity and global efficiency ($0.82$)
  • Strong negative correlation between average node degree and mean shortest path ($-0.77$)
  • Strong positive correlation between average edge betweenness, path length, and diameter ($>0.88$)
  • Restricted average correlation between metrics (mean absolute coefficient $\sim 0.35$), supporting metric complementarity.
• Nineteen networks are flagged as metric outliers and preserved to permit evaluation of algorithms under rare or extremal design conditions.

5. Applications and Future Guidance

The Topology Bench resource and methodology directly enable:

• Rigorous Algorithm Benchmarking: Researchers can evaluate new routing, survivability, and optimization algorithms across a broad, representative, and well-characterized topology set.
• Dataset Generalization and Fairness: Objective, cluster-based selection ensures results are not biased toward atypical topologies (e.g., overused exemplars like NSFNET), with synthetic augmentation for unrepresented scenarios.
• Scalability Testing: The inclusion of large synthetic graphs facilitates experimental exploration of scaling behavior, resilience thresholds, and sensitivity to topological perturbations.
• Outlier Identification for Stress Testing: The presence of outlier topologies in the dataset explicitly broadens the test space for robustness and real-world anomaly response.

6. Dataset Format and Accessibility

All topologies, real and synthetic, are distributed in standardized CSV format, ensuring compatibility and ease of integration into graph libraries and simulation tools. Each record includes essential topological attributes, spatial coordinates, and, for synthetic graphs, model parameters and validation status.

A summary table of essential dataset and metric aspects:

Aspect	Details
Metrics	Node degree, density, path length, diameter, clustering, betweenness, global efficiency, spectra
Real-world set	105 geolocated, planarity/resilience marked, multi-scale
Synthetic set	270,900 SNR-BA, exhaustive in $n$, $d$, geographic scale
Selection method	K-means clustering over nine “optimal” metrics; coverage per cluster
Correlation	Key pairs identified, moderate mean inter-metric correlation
Application advice	Select one network per cluster, augment with synthetics for spectrum coverage, include outliers in stress

7. Implications for Optical Network Research

The Topology Bench initiative provides a foundation for reproducible, equitable benchmarking and systematic exploration of graph topology utilization in optical networks. By foregrounding a metric-driven, clustering-informed selection regime, optical network research attains improved statistical validity, fairness, and interpretability, while uncovering gaps in empirical diversity that can be explicitly addressed through targeted synthetic data generation. This approach is extensible to other infrastructure domains where topology critically shapes performance, reliability, and scalability.