# Realistic Aspects of Simulation Models for Fake News Epidemics over Social Networks
## 4 Results
### Impact of Influencers and Bots  
We start with Figure 5, which shows the results of simulations in two different scenarios through three plots. In the top row, SBFC plots shows the variation of the number of susceptible (blue), believer (orange), and fact-checker nodes (green) throughout the duration of the simulation, expressed in seconds.  
Figure 5: SBFC plots (**top row**), network infection graphs (**middle row**), and network recovery graphs (**bottom row**) for fake news spread in simulated online social networks (OSNs). (**Left**) Baseline network. (**Right**) Baseline network plus 30 influencers and 10 bots. In the middle row, the darker a node’s color is, the earlier that node starts believing in the fake news item. In the bottom row, the darker a node’s color is, the earlier that node performs fact-checking.  
In the middle row, we show the spreading of the fake news over the network (drawn without edges for better readability). The color of each node denotes its average infection time, where the fake news starts spreading from the same node over the same network (i.e., with always the same first believer). A node depicted with a dark color is typically infected shortly after the start of the simulation, whereas a light-colored one is typically infected much later. In the third row, the graphs similarly show the average time of recovery. The darker the color is, the faster the recovery is.  
For this first comparison, we considered both our baseline network composed only of common nodes (left column in Figure 5) and a network that additionally has 30 influencers and 10 bots. We constructed the SBFC plots by averaging the results of 400 simulations. In particular, we generated 50 different network topologies at random using the same set of parameters; these networks are the same for both our set of simulations, in order to obtain comparable results. Then, we executed eight simulations for each topology. Instead, for the infection and recovery time graphs, we computed the corresponding average times over a set of 100 simulations.  
In the baseline network, the spreading is slow and critically affects only part of the network. The B curve (orange) reaches a peak of about 750 believer nodes simultaneously present in the network and then decreases, quenched by the debunking and fact-checking processes (FC, green curve). Adding influencers and bots accelerates the infection and helps both the fake news and the debunking spread out to more nodes.  
In particular, with 2000 common nodes and 30 influencers, fake news spreading infects (on average) almost half of the common nodes. When 10 bots are further added to the network (right column in Figure 5), the spreading is faster, and after a short amount of time, the majority of the common nodes believe in the fake news. The SBFC plot in the top-right panel shows that the fake news reaches more than 80% of the network nodes, whereas the middle panel confirms that infections occur typically early in the process, with the exception of a few groups of nodes that get infected later on. Similarly, it takes more time to recover from the fake news and perform fact-checking than in the baseline case (bottom-right graph).  
The above simulations already confirm the strong impact influencers and bots may have on fake news spreading: influencers make it possible to convey fake news through their many out-connections, and reach otherwise secluded portions of the population. Bots, by insisting on spreading fake news, increase the infection probability early on in the fake news spreading process. As a result, the effectiveness of the fake news is higher, and more agents become believers before the debunking process starts to create fact-checkers.