# 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 c c c} \hline \hline  & \multicolumn{2}{c}{**Facebook (20\%)**} & \multicolumn{2}{c}{**Github (20\%)**} & \multicolumn{2}{c}{**Google+ (10\%)**} & \multicolumn{2}{c}{**Youtube (10\%)**} \\ \hline  & **full** & \(d>\)**mean** & **full** & \(d>\)**mean** & **full** & \(d>\)**mean** & **full** & \(d>\)**mean** \\ \hline Metropolis-Hastings & 0.118 & 0.127 & 0.174 & 0.059 & 0.216 & 0.105 & 0.237 & 0.020 \\ CNRW & 0.227 & 0.053 & 0.278 & 0.076 & 0.591 & 0.153 & 0.362 & 0.178 \\ CNARW & 0.181 & 0.038 & 0.273 & 0.065 & 0.489 & 0.161 & 0.353 & 0.141 \\ Forest Fire & 0.160 & 0.016 & 0.281 & 0.059 & 0.529 & 0.102 & 0.318 & 0.141 \\ \hline
**Fireball** & 0.266 & 0.077 & 0.306 & 0.077 & 0.557 & 0.113 & 0.396 & 0.169 \\
**Edgeball** & 0.268 & 0.084 & 0.211 & 0.035 & 0.638 & 0.164 & 0.342 & 0.169 \\
**Hubball** & 0.243 & 0.096 & 0.112 & 0.027 & 0.573 & 0.140 & 0.279 & 0.099 \\
**Coreball** & 0.537 & 0.183 & 0.520 & 0.056 & 0.702 & 0.188 & 0.499 & 0.223 \\ \hline Snowball & 0.224 & 0.082 & 0.073 & 0.022 & 0.482 & 0.052 & 0.279 & 0.125 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Kolmogorov-Smirnov test for degree distribution similarity (lower is closer) for the Facebook and Github graphs sampled at 20%, Google+ and Youtube graphs sampled at 10%. The degree distribution is considered either fully (“full” column) or for high-degree (greater than the mean degree of all nodes in the graph) nodes only. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Sampling Method** & \multicolumn{2}{c}{**Avg. Clustering Coef.**} & **Transitivity Ratio** & **PageRank Ratio** & **Density** \\ \hline Metropolis-Hastings & 10\% & 0.420 (16.83\%) & 0.405 (76.25\%) & 1.490 & \(4.91\times 10^{-3}\) \\  & 20\% & 0.409 (12.57\%) & 0.330 (42.15\%) & 1.463 & \(3.08\times 10^{-3}\) \\ \hline CNRW & 10\% & 0.464 (29.06\%) & 0.337 (45.15\%) & 2.007 & \(9.52\times 10^{-3}\) \\  & 20\% & 0.445 (23.78\%) & 0.299 (28.66\%) & 1.771 & \(5.22\times 10^{-3}\) \\ \hline CNARW & 10\% & 0.369 (2.49\%) & 0.287 (23.42\%) & 2.057 & \(7.99\times 10^{-3}\) \\  & 20\% & 0.375 (4.19\%) & 0.274 (17.77\%) & 1.757 & \(4.75\times 10^{-3}\) \\ \hline Forest fire & 10\% & 0.320 (11.10\%) & 0.291 (25.23\%) & 1.773 & \(8.49\times 10^{-3}\) \\  & 20\% & 0.411 (14.37\%) & 0.275 (18.42\%) & 1.600 & \(4.46\times 10^{-3}\) \\ \hline
**Fireball** & 10\% & 0.413 (14.82\%) & 0.303 (30.32\%) & 1.887 & \(1.09\times 10^{-2}\) \\  & 20\% & 0.392 (8.95\%) & 0.254 (9.12\%) & 1.650 & \(5.96\times 10^{-3}\) \\ \hline
**Edgeball** & 10\% & 0.441 (22.59\%) & 0.238 (2.44\%) & 1.854 & \(1.50\times 10^{-2}\) \\  & 20\% & 0.449 (24.73\%) & 0.257 (10.53\%) & 1.664 & \(6.23\times 10^{-3}\) \\ \hline
**Hubball** & 10\% & 0.484 (34.46\%) & 0.220 (5.51\%) & 1.805 & \(1.41\times 10^{-2}\) \\  & 20\% & 0.460 (27.94\%) & 0.223 (4.02\%) & 1.619 & \(6.46\times 10^{-3}\) \\ \hline
**Coreball** & 10\% & 0.476 (32.32\%) & 0.291 (25.39\%) & 2.030 & \(1.97\times 10^{-2}\) \\  & 20\% & 0.461 (28.23\%) & 0.300 (29.20\%) & 1.823 & \(7.57\times 10^{-3}\) \\ \hline Snowball & 10\% & 0.373 (3.81\%) & 0.245 (5.66\%) & 1.750 & \(1.22\times 10^{-2}\) \\  & 20\% & 0.399 (10.87\%) & 0.243 (4.48\%) & 1.660 & \(5.69\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Numerical results for the Facebook graph sampled at 10% and 20%. Full graph’s average clustering coefficient is 0.36, transitivity ratio is 0.23, density is \(6.7\times 10^{-4}\). Relative error for the average clustering coefficient and transitivity ratio is shown between parentheses. We also introduce another metric called _interCommunity VIP score_ or _IVIP_ score that summarizes better the intent we have, i.e., sampling efficiently the influencers in social networks. First a community