# On Simulating the Propagation and Countermeasures of Hate Speech in Social Networks
## 6 Simulation Results  
We used NetLogo multi-agent modeling environment ([[http://cl.northwestern.edu/netlogo/](http://cl.northwestern.edu/netlogo/)]([http://cl.northwestern.edu/netlogo/](http://cl.northwestern.edu/netlogo/)), accessed on 1 November 2021) to implement our model. The resulting simulator is publicly available (see Data Availability Statement) together with the tests we carried out to analyse the simulation results and the obtained data (associated tests and resulting simulation data are also publicly available). As introduced by Section 4, the simulation is conducted in two phases. First, the network construction phase (see Section 4.1) is run until \(t_{1}\in[0,500,1000,2000,5000]\) rounds (ticks), which creates a network with about as many user nodes (more precisely, since we start with an initial network of two nodes and we add one network node per round, then the network finishes this phase having a size of \(t_{1}+2\) nodes). Then, our opinion dynamics phase from Section 4.2 starts so that the network is grown for further 1000 rounds. Figure 7 depicts a screenshot of opinion diffusion in our simulation where both hateful and non-hateful posts are being distributed. Both posts and reposts are represented as solid circles, so our visualization (the graph layout algorithm is based on the Fruchterman-Reingold layout algorithm [50]) does not distinguish the publishing of original content from its subsequent reposting. Moreover, the direction of links indicates influence: we signal that a followee user A influences its follower B by a directed arrow (i.e., a link in the model) that goes from A to B. Thus, the amount of out-going links (i.e., the out-degree) of a user node corresponds to its amount of followers. Each simulation is conducted 100 times for building the following average metrics:  
* Fractions of normal and hateful persons, which correspond, respectively, to the proportion of the normal and hateful persons over the whole network population. * Fractions of normal and hateful posts: the proportion of posts authored by hateful and normal users over the whole amount of posts that exist at the current round. Notice that the amount of posts per round can be much higher than the amount of existing persons, because of the possibility to repost multiple posts from the own neighbours. * Mean and standard deviation of hate score distribution within the society. * Ratio of network densities of hateful over normal users, which shows how much the group of hateful users is more cohesive than the group of normal users. Network density for each group is computed as the division of _actual_connections/potential_connections_, where _potential_connections_\(=n(n-1)/2\) and \(n\) is the network population. The overall ratio is then computed as the division of both network densities: _densities_ratio_ = _network_density_haters/network_density_normals_. * Reciprocity of following within normal or hateful users. When two users follow each other (i.e., a followee back-follows its follower) we count these two links as one reciprocal connection. Then, we compute the number of reciprocal connections divided by all connections within a specific group--be it the haters or the group of normal users. * Mean followers and mean followees, e.g., mean followers corresponds to the average amount of out-going influence connections over a group of (hateful or normal) persons. * Mean ratio follower/followee: the average of _out-going/in-coming_ influence connections. This metric shows the connectivity profile in terms of following relations and is of interest because haters are known to have less followers than the following connections their create. * Mean path length of reposts through the network: the average over all post path lengths through the network. It is computed considering that each post generates multiple paths if reposted by different followers. * Fraction of swaps to a hateful society: proportion of runs which end with a swap (i.e., having more than 30% of hateful users, see Section 3).