# Building Topic-Driven Virtual IoTs in a Multiple IoTs Scenario
## 6 Experiments
### Average Fraction of Merged C-Nodes and Analysis of Node Distribution in Virtual IoTs  
Another quality parameter for virtual IoTs returned by our approach regards the average number of merged c-nodes present in each of them. Indeed, the presence of merged c-nodes in an IoT is an indicator of the fact that this IoT is capable of connecting concepts coming from different real IoTs, and, therefore, from concepts whose relationships would have been uncaptured otherwise, or, in other words, that the knowledge it is presenting is new and did not exist previously. Clearly, the higher the fraction of merged c-nodes and the higher the fraction of different original IoTs they belong to, the higher the connecting capability of virtual IoTs. Also for this experiment, we considered the ten MIoTs described in Section 6.2 and performed the same tasks illustrated therein for both the supervised and the unsupervised approaches. The obtained results are reported in Tables 5-7. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**MIoT (Size)**} & \multicolumn{2}{c}{**Average Clustering Coefficient**} & \multicolumn{2}{c}{**Average Density**} \\ \cline{2-5}  & **Real IoTs** & **Virtual IoTs** & **Real IoTs** & **Virtual IoTs** \\ \hline \(\mathcal{M}_{1}\) (176) & 0.230 & 0.473 & 0.348 & 0.315 \\ \(\mathcal{M}_{2}\) (301) & 0.272 & 0.499 & 0.262 & 0.350 \\ \(\mathcal{M}_{3}\) (485) & 0.293 & 0.500 & 0.274 & 0.375 \\ \(\mathcal{M}_{4}\) (778) & 0.353 & 0.511 & 0.269 & 0.318 \\ \(\mathcal{M}_{5}\) (946) & 0.372 & 0.509 & 0.276 & 0.316 \\ \(\mathcal{M}_{6}\) (1256) & 0.385 & 0.506 & 0.284 & 0.314 \\ \(\mathcal{M}_{7}\) (1725) & 0.386 & 0.522 & 0.280 & 0.328 \\ \(\mathcal{M}_{8}\) (2028) & 0.388 & 0.535 & 0.273 & 0.360 \\ \(\mathcal{M}_{9}\) (3544) & 0.394 & 0.547 & 0.271 & 0.364 \\ \(\mathcal{M}_{10}\) (5024) & 0.398 & 0.562 & 0.269 & 0.368 \\ \hline \end{tabular}
\end{table} 
Table 4: Values of both clustering coefficient and density of real and virtual IoTs against the size of MIoTs (unsupervised approach). From the analysis of these tables, we observe that both the supervised and the unsupervised approaches return satisfying results. As for the supervised approach, we can observe that the fraction of merged c-nodes increases when the size of MIoT increases. Furthermore, we can also observe a slight increase of this fraction when \(|Q|\) increases. The same trends can be observed for the average fraction of involved real IoTs, even if, for this parameter, its increase against the increase of \(|Q|\) is more pronounced. As for the unsupervised approach, we can observe that the average fraction of merged nodes is always very high, independently of the MIoT size. By contrast, in this case, the fraction of involved real IoTs is quite high even if lower than the ones generally observed for the supervised approach. Furthermore, its value does not significantly change when the MIoT size increases. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**MIoT (Size)**} & \multicolumn{5}{c}{**Average Fraction of Involved Real IoTs**} \\ \cline{2-6}  & \(|Q|=1\) & \(|Q|=2\) & \(|Q|=4\) & \(|Q|=6\) & \(|Q|=8\) & \(|Q|=10\) \\ \hline \(\mathcal{M}_{1}\) (176) & 0.373 & 0.467 & 0.488 & 0.476 & 0.452 & 0.448 \\ \(\mathcal{M}_{2}\) (301) & 0.365 & 0.469 & 0.525 & 0.501 & 0.488 & 0.480 \\ \(\mathcal{M}_{3}\) (485) & 0.482 & 0.477 & 0.448 & 0.442 & 0.435 & 0.432 \\ \(\mathcal{M}_{4}\) (778) & 0.457 & 0.432 & 0.418 & 0.415 & 0.413 & 0.411 \\ \(\mathcal{M}_{5}\) (946) & 0.455 & 0.482 & 0.624 & 0.628 & 0.647 & 0.644 \\ \(\mathcal{M}_{6}\) (1256) & 0.453 & 0.514 & 0.805 & 0.864 & 0.917 & 0.924 \\ \(\mathcal{M}_{7}\) (1725) & 0.482 & 0.577 & 0.815 & 0.872 & 0.917 & 0.924 \\ \(\mathcal{M}_{8}\) (2028) & 0.514 & 0.672 & 0.833 & 0.898 & 0.917 & 0.924 \\ \(\mathcal{M}_{9}\) (3544) & 0.584 & 0.704 & 0.844 & 0.905 & 0.924 & 0.926 \\ \(\mathcal{M}_{10}\) (5024) & 0.624 & 0.727 & 0.888 & 0.911 & 0.928 & 0.934 \\ \hline \hline \end{tabular}
\end{table}