Fig. 3

Features of the optimal communication networks for different H and R_FN values. The three pictures in all the four subfigures are the following: (i) the graphic representation of the optimal communication network, (ii) the weighted in and out degree distribution of the optimal communication network, and (iii), the observation activity values as a function of the communication activity values. In order to retrieve a more intuitive representation of the optimal communication network, we have omitted the edges with very small weights (the ones smaller than \(\frac {0.3}{N}=0.01\)). As it can be seen in the insets entitled “Weighted degree distribution”, the weighted in-degree values are very similar for all nodes, independently of H or the fake news ratio (green bars). However, exposure to fake news (bottom row, subfigures c and d) results in smaller weighed in-degree values (the green bars are shifted towards smaller values). Furthermore, exposure to false information or high values of H (subfigures b and d) calls forth “blurred” out-degree distribution (magenta color), marking the differentiation of agents regarding their role in spreading the information, which phenomenon can not be observed in subfigure a. Agents with zero or close-to-zero communication activity values are the peripheral nodes on the graphs who are connected to the rest of the group only via in-coming edges