# On Simulating the Propagation and Countermeasures of Hate Speech in Social Networks
## 3 Terminology  
This section is devoted to introduce the terminology required to properly describe our models.  
**Hate score** is the central metric in our work and represents the users' attitude and opinion about some polarised topic, which is discussed within a social network. For instance, immigration laws or equal rights of men and women. It is a real number in \([0,1]\), where both extremes correspond to a very non-hateful and hateful opinions, respectively. We use the hate score as a user opinion value in our diffusion models but also as a threshold to characterise users. The same concept was also employed by [PERSON] et al. [6] who showed that hate score distribution on Gab is positively biased towards a non-hateful stance. Similarly, we define a user as hateful when _hate score_\(\geq\) 0.75 and signal it as a red dot in the network graphical representation (see Figure 1). Otherwise, (i.e., when _hate score_\(<\) 0.75) we assume the user to be normal and represent it as a black dot. We take this threshold in accordance to--and for better comparability with--previous work. As stated before, the amount of haters is known to be a minority of ca. 1%. Therefore, we model the hate score using the Gamma distribution \(\Gamma(\alpha,\lambda)\) as depicted in Figure 2, so that the area under curve for \(x>0.75\) is ca. 0.01. For those rare cases when the Gamma distribution naturally exceeds the value of 1 we artificially set users' hate score to the extreme stance of 1.  
**Hate core** is a network component consisting of densely connected hateful users. Figure 1 depicts how most hateful users (in red) are clustered together. Such components emerge from the high cohesiveness among hateful users as well as from their higher activity. It is also worth noticing that, although single users within a hate core do not exhibit the same influence as some famous mainstream users, as a compound, the hate core can achieve similar effects on the network and attract other users.  
Figure 1: **Hate core**: Densely connected hateful users (red nodes) within the overall network mostly formed by normal users (black nodes).  
**Hate strains** are extensions of hate cores. As illustrated by Figure 3, hate strains consist of connected hateful users, but exhibit less network density among them than the hate core that originated them. Most often, hate strains emerge from a hate core as the result of opinion diffusion under the negative influence of the hateful users in the core.  
**Swap to a hateful society** (by society we mean all the users in the social network). We identify such network transformation when hateful content floods the network and leads to a swap in the opinion of a significant number of users. In particular, we consider a society to be very hateful when the amount of hateful users exceeds 30% of all users in the social network. In fact, experiments have shown that after having trespassed this 30% limit, it becomes extremely difficult to return to a non-hateful society within the time scope of our simulation. Thus, although there may be some exceptions (as hate spread could still be stopped if strategical nodes with high influence within a hateful group were convinced to become non-hateful), we consider swap to a hateful society as the outcome of an irreversible process, which destabilises the society in a very severe way.