# Strategies of Success for Social Networks: Mermaids and Temporal Evolution
## 5 Experimental Results
### Results
In particular, we fixed the number of mermaids (\(m=6\) and \(m=12\)) and checked the performance of other configurations compared to the baseline (that are \((6,10,10)\) and \((12,10,10)\) respectively). The plots presented are grouped by network (Communities and VirtualTourist). Figures 17-19 show the results obtained for Communities and consider different mermaids' dynamics, namely broadcast, word of mouth, and preferential. Table 5 then summarizes the \(T_{min}\) for all the various configurations. Conversely, Figures 20-22 refer to VirtualTourist, and Table 6 summarizes the corresponding \(T_{min}\)'s. All the plots presented in this section clearly show that increasing \(C_{s}\) results in shrinking times to obtain the target efficiency. This is a very interesting result because it confirms the effectiveness of employing more mermaids in order to boost network engagement and in particular to lower the threshold after which the connectivity spreads all over the network. Indeed, another interesting observation could be made. We note that even though increasing \(C_{s}\) always triggers a broader connectivity distribution, the benefit is not proportional to \(C_{s}\). For instance, quadrupling \(C_{s}\), the simulated time shrinks less than four times. The question Q3 will account for quantitatively defining this benefit. Remarkably, the observed effects are universal in the sense that they hold regardless of the network and the considered rule, suggesting their validity in a wide class of social networks. Figure 7:2 Accelerated analysis with mermaids fixing the number of mermaids to \(m=6\) and \(m=12\), random, aristocratic, and social rules. The mermaids’ dynamics evolve according to the _preferential_ model. Communities online social network. Figure 7:3 Accelerated analysis with mermaids fixing \(m=6\) (**top plots**) and \(m=12\) (**bottom plots**), random, aristocratic, and social rules, _word of mouth model_ (for mermaids’ dynamics). Communities online social network. Figure 7:4 Effect on parameters’ variation on the configurations fixing the number of mermaids to \(m=6\) (**top panels**) and \(m=12\) (**bottom panels**). Four cost levels are then considered in each plot, from 600 to 4800. _Broadcast model_, VirtualTourist online social network. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**CM** & **bro md** & **bro ari** & **word md** & **word ai** & **word soc** & **pref rnd** & **pref ari** & **pref soc** \\ \hline (no mermaids) & 1381 & 1930 & 1381 & 1930 & 1328 & 1381 & 1930 & 1328 \\ (6,10,10) & 112.92 & 128.16 & 111.66 & 126.95 & 113.01 & 106.82 & 118  
**Q3: Trade-off between the benefit of investing on mermaids and the cost**. In the plots presented previously, we described how the timespan needed to get the reference efficiency varies according to \(C_{s}\). Figures 23 and 24 (rightmost panels) show \(T_{min}\) as a function of \(C_{s}\) and this allows to describe more quantitatively the benefit of investing on mermaids. In fact, plots clearly show that this is not linear as one might guess, instead it is inversely proportional as \(C_{s}\). We think this is probably due to the system saturation. In other words, the network is not able to respond to high level of exogenous stimuli from mermaids resulting in performances that are comparatively similar to those obtained with lower cost configurations. Figure 7:5 Accelerated analysis with mermaids fixing \(m=6\) and \(m=12\), random, aristocratic, and social rules, _word of mouth model_ (for mermaids’ dynamics), VirtualTourist online social network. Figure 7:6 Accelerated analysis with mermaids fixing \(m=6\) and \(m=12\), with random, aristocratic, and social rules, _preferential model_ (for mermaids’ dynamics), VirtualTourist online social network. In order to test whether this finding holds when considering threshold values of efficiency, we investigated the time needed to get half \(E_{glob}\) and one third \(E_{glob}\). Surprisingly, as the figures show (left