Table 2. Runtimes for distance various distance measures, for graphs of size n = 100 and n = 300.
Each distance is calculated N = 500 times. Each sample generates two Erdős-Rényi random graphs with parameter p = 0.15, and times the calculation of the distance between the two graphs. All distances are implemented in the NetComp library, which can be found on GitHub at [75].
| Distance Measure | Computational Time (n = 100) |
| Edit Distance | 8.2 × 10−5 ± 4.5 × 10−5 |
| DeltaCon | 3.1 × 10−3 ± 7.4 × 10−4 |
| Resistance Dist. | 7.5 × 10−3 ± 1.4 × 10−3 |
| Spectral (Adjacency) | 1.1 × 10−2 ± 1.1 × 10−3 |
| Spectral (Laplacian) | 1.2 × 10−2 ± 4.7 × 10−3 |
| Spectral (Normalized Laplacian) | 1.5 × 10−2 ± 9.4 × 10−4 |
| NetSimile | 2.3 × 10−1 ± 6.3 × 10−2 |
| Distance Measure | Computational Time (n = 300) |
| Edit Distance | 5.7 × 10−4 ± 9.9 × 10−4 |
| DeltaCon | 1.4 × 10−2 ± 6.6 × 10−3 |
| Resistance Dist. | 8.8 × 10−2 ± 5.4 × 10−2 |
| Spectral (Adjacency) | 1.5 × 10−1 ± 8.9 × 10−3 |
| Spectral (Laplacian) | 1.5 × 10−1 ± 9.8 × 10−3 |
| Spectral (Normalized Laplacian) | 1.6 × 10−1 ± 6.6 × 10−3 |
| NetSimile | 5.5 × 10−1 ± 1.1 × 10−2 |
| Distance Measure | Computational Time (n = 1, 000) |
| Edit Distance | 4.2 × 10−3 ± 1.5 × 10−3 |
| DeltaCon | 8.8 × 10−2 ± 6.4 × 10−3 |
| Resistance Dist. | 5.9 × 10−1 ± 4.3 × 10−2 |
| Spectral (Adjacency) | 1.3 ± 5.5 × 10−1 |
| Spectral (Laplacian) | 1.3 ± 1.6 × 10−1 |
| Spectral (Normalized Laplacian) | 1.4 ± 3.7 × 10−1 |
| NetSimile | 2.5 ± 1.8 × 10−1 |