# Building Topic-Driven Virtual IoTs in a Multiple IoTs Scenario
## 6 Experiments
### Colhesion of the Obtained Topic-Guided Virtual IoTs
#### 6.2.1 Supervised Approach  
In this test, we run our supervised approach on ten MIoTs, \(\mathcal{M}_{1}\),..., \(\mathcal{M}_{10}\), consisting of 176, 301, 485, 778, 946, 1256, 1725, 2028, 3544 and 5024 nodes. Clearly, the number of IoTs for each MIoT was equal to six, one for each area of the city of Porto that we have defined. For each MIoT, we submitted a set of 10 queries consisting of 1 (resp., 2, 4, 6, 8 and 10) word(s).  
Each query returned a virtual thematic IoT for which we computed the corresponding clustering coefficient and density. Finally, we averaged the obtained results for each MIoT and for each set of queries, and we compared them with the average clustering coefficient and the average density of the corresponding real IoTs. The obtained results are reported in Tables 2 and 3.  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**MIoT (Size)**} & \multirow{2}{*}{**Avg. Clustering Coeff. (Real IoTs)**} & \multicolumn{6}{c}{**Avg. Clustering Coeff. (Virtual IoTs)**} \\ \cline{3-8}  & & \(|Q|=1\) & \(|Q|=2\) & \(|Q|=4\) & \(|Q|=6\) & \(|Q|=8\) & \(|Q|=10\) \\ \hline \(\mathcal{M}_{1}\) (176) & 0.230 & 0.318 & 0.368 & 0.389 & 0.394 & 0.401 & 0.408 \\ \(\mathcal{M}_{2}\) (301) & 0.272 & 0.343 & 0.388 & 0.419 & 0.424 & 0.434 & 0.446 \\ \(\mathcal{M}_{3}\) (485) & 0.293 & 0.396 & 0.437 & 0.477 & 0.482 & 0.488 & 0.497 \\ \(\mathcal{M}_{4}\) (778) & 0.353 & 0.447 & 0.478 & 0.503 & 0.508 & 0.511 & 0.517 \\ \(\mathcal{M}_{5}\) (946) & 0.371 & 0.452 & 0.492 & 0.512 & 0.522 & 0.524 & 0.526 \\ \(\mathcal{M}_{6}\) (1256) & 0.385 & 0.486 & 0.511 & 0.529 & 0.530 & 0.532 & 0.535 \\ \(\mathcal{M}_{7}\) (1725) & 0.386 & 0.501 & 0.524 & 0.536 & 0.537 & 0.538 & 0.539 \\ \(\mathcal{M}_{8}\) (2028) & 0.388 & 0.519 & 0.536 & 0.541 & 0.541 & 0.542 & 0.543 \\ \(\mathcal{M}_{9}\) (3544) & 0.392 & 0.522 & 0.540 & 0.544 & 0.544 & 0.545 & 0.546 \\ \(\mathcal{M}_{10}\) (5024) & 0.395 & 0.534 & 0.546 & 0.546 & 0.546 & 0.547 & 0.548 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Values of the clustering coefficient for real and virtual IoTs against the size of MIoTs and queries used to generate the virtual IoTs (supervised approach).  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**MIoT (Size)**} & \multirow{2}{*}{**Average Density (Real IoTs)**} & \multicolumn{6}{c}{**Average Density (Virtual IoTs)**} \\ \cline{3-8}  & & \(|Q|=1\) & \(|Q|=2\) & \(|Q|=4\) & \(|Q|=6\) & \(|Q|=8\) & \(|Q|=10\) \\ \hline \(\mathcal{M}_{1}\) (176) & 0.348 & 0.260 & 0.264 & 0.280 & 0.289 & 0.296 & 0.301 \\ \(\mathcal{M}_{2}\) (301) & 0.262 & 0.292 & 0.303 & 0.309 &From the analysis of these tables, we can observe that, in almost all circumstances, the values of both clustering coefficient and density are higher or much higher for the virtual thematic IoTs than for the real ones. This is clearly a confirmation of the goodness of our supervised approach, which returns topic-guided IoTs more cohesive than the original ones. We also observe that when \(|Q|\) increases, the values of both clustering coefficient and density increases. This can be explained by observing that, in processing \(Q\), our approach takes the portions of networks containing at least one keyword of \(Q\). When \(|Q|\) increases, the portion of networks selected by our approach increases too, and the probability of selecting a very high number of edges (i.e., a number so high to lead to an increase of clustering coefficient and density) increases as well.