# Spikyball Sampling: Exploring Large Networks via an Inhomogeneous Filtered Diffusion
## 5 Experimental Evaluation
### Comparing to the Literature
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Sampling Method** & **Avg. Clustering Coef.** & **Transitivity Ratio** & **PageRank Ratio** & **Density** \\ \hline Metropolis-Hastings & 0.115 (4.24\%) & 0.052 (487.46\%) & 2.930 & \(2.07\times 10^{-4}\) \\ CNRW & 0.153 (93.22\%) & 0.040 (354.69\%) & 4.201 & \(4.65\times 10^{-4}\) \\ CNARW & 0.125 (13.55\%) & 0.041 (364.51\%) & 4.210 & \(4.58\times 10^{-4}\) \\ Forest fire & 0.146 (32.40\%) & 0.035 (299.01\%) & 4.050 & \(4.05\times 10^{-4}\) \\ \hline
**Fireball** & 0.154 (40.13\%) & 0.038 (332.71\%) & 3.967 & \(4.90\times 10^{-4}\) \\
**Edgeball** & 0.186 (69.20\%) & 0.028 (221.57\%) & 3.886 & \(4.57\times 10^{-4}\) \\
**Hubball** & 0.306 (177.98\%) & 0.009 (6.58\%) & 3.219 & \(3.74\times 10^{-4}\) \\
**Coreball** & 0.143 (30.13\%) & 0.038 (331.17\%) & 4.526 & \(5.91\times 10^{-4}\) \\ \hline Snowball & 0.294 (167.08\%) & 0.009 (3.64\%) & 3.620 & \(3.81\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Numerical results for the Youtube graph sampled at 10%. Full graph’s average clustering coefficient is 0.11, transitivity ratio is \(8.8\times 10^{-3}\), density is \(1.57\times 10^{-5}\). Relative error for the average clustering coefficient and transitivity ratio is shown between parentheses. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Sampling Method** & **Avg. Clustering Coef.** & **Transitivity Ratio** & **PageRank Ratio** & **Density** \\ \hline Metropolis-Hastings & 10\% & 0.110 (34.64\%) & 0.056 (355.32\%) & 2.070 & \(2.56\times 10^{-3}\) \\  & 20\% & 0.166 (1.22\%) & 0.032 (160.00\%) & 2.096 & \(2.18\times 10^{-3}\) \\ \hline CNRW & 10\% & 0.237 (41.31\%) & 0.061 (397.52\%) & 3.763 & \(6.74\times 10^{-3}\) \\  & 20\% & 0.214 (27.73\%) & 0.041 (227.87\%) & 2.631 & \(3.55\times 10^{-3}\) \\ \hline CNARW & 10\% & 0.211 (25.79\%) & 0.061 (397.22\%) & 3.778 & \(6.75\times 10^{-3}\) \\  & 20\% & 0.186 (10.72\%) & 0.041 (232.39\%) & 2.645 & \(3.54\times 10^{-3}\) \\ \hline Forest fire & 10\% & 0.238 (41.91\%) & 0.063 (408.04\%) & 3.656 & \(6.30\times 10^{-3}\) \\  & 20\% & 0.190 (13.41\%) & 0.038 (207.28\%) & 2.607 & \(3.59\times 10^{-3}\) \\ \hline
**Fireball** & 10\% & 0.246 (46.53\%) & 0.048 (288.58\%) & 3.243 & \(5.45\times 10^{-3}\) \\  & 20\% & 0.207 (23.26\%) & 0.040 (225.95\%) & 2.583 & \(3.75\times 10^{-3}\) \\ \hline
**Edgeball** & 10\% & 0.310 (85.18\%) & 0.040 (223.09\%) & 3.036 & \(4.65\times 10^{-3}\) \\  & 20\% & 0.247 (47.28\%) & 0.035 (184.11\%) & 2.452 & \(3.09\times 10^{-3}\) \\ \hline
**Hubball** & 10\% & 0.373 (122.79\%) & 0.025 (98.76\%) & 2.594 & \(3.94\times 10^{-3}\) \\  & 20\% & 0.348 (107.42\%) & 0.020 (61.37\%) & 2.092 & \(2.48\times 10^{-3}\) \\ \hline
**Coreball** & 10\% & 0.252 (50.12\%) & 0.054 (337.38\%) & 4.247 & \(1.05\times 10^{-2}\) \\  & 20\% & 0.188 (12.06\%) & 0.039 (214.62\%) & 2.968 & \(4.84\times 10^{-3}\) \\ \hline Snowball & 10\% & 0.435 (159.64\%) & 0.023 (86.65\%) & 2.987 & \(4.28\times 10^{-3}\) \\  & 20\% & 0.393 (134.28\%) & 0.019 (49.94\%) & 2.027 & \(2.48\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Numerical results for the Github graph sampled at 10% and 20%. Full graph’s average clustering coefficient is 0.168, transitivity ratio is \(1.24\times 10^{-2}\), density is \(4.07\times 10^{-4}\). Relative error for the average clustering coefficient and transitivity ratio is shown between parentheses.