# Toward a Standard Approach for Echo Chamber Detection: Reddit Case Study
## 4 Reddit: Politics, Gun Control, and Minorities Discrimination
### Homogeneous, Meso-Scale, Users' Clusters Identification  
Once we have defined labeled interaction networks, we focus on discovering if they present cohesive meso-scale topologies both from a structural and ideological perspective. Following the rationale in Section 3.4, we rely on Eva, a CD algorithm belonging to Labeled Community Detection approaches. Eva is tailored to detect communities both maximizing their internal density through Modularity (see Definition 2) and their labels homogeneity relying on Purity (see Definition 3). Accordingly, we apply Eva to each topic and semester, thus identifying our candidate communities. Then, we evaluate them by means of Conductance (see Definition 4) and Purity. In this case study, we set the Conductance score \(\leq 0.5\) to ensure that more than half of the total edges remain within the community boundaries. Meanwhile, for Purity, we set a threshold equal to 0.7 to make sure that most of the users in an echo chamber share the same ideological label. In Figure 3 we show the communities evaluation process for Gun Control, minorities discrimination, and Political Sphere topics. In each scatter plot, we can classify as echo chambers those communities that lie above the horizontal red line. The difference in results between the three topics is stark. Gun Control (Figure 3a) does not present strongly polarized communities among different semesters. Indeed, on average, only 6.7% of total users fall in an echo chamber. Among them, 97.1% of members show a Pro-Trump tendency (i.e., in the first semester), while only the 2.9% have an Anti-Trump leaning (i.e., in the fourth semester). Moreover, we can observe that Pro-Trump users tend to form communities composed of like-minded individuals, even if not sufficiently ideologically homogeneous. Instead, Anti-Trump users mainly interact with the opposite side of the controversy, probably because they are a minority with respect to the totality of users (see Table 4). As regards minorities discrimination (Figure 3b), the overall scenario is definitely different. Indeed, on average, more than half of total users (i.e., 53.8%) are trapped in echo chambers. Further, we can observe in all semesters both Pro-Trump and Anti-Trump ECs, even if the first group outnumbered the second (i.e., 85% of Pro-Trump ECs members and 15% of Anti-Trump ones). Moreover, different from the other two topics, this one presents more than one EC of the same ideological leaning. On the other hand, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Topic** & **\# Nodes** & **\# Edges** & **Density** & **\# Pro-Trump** & **\# Anti-Trump** & **\# Neutral** \\ \hline Gun Control & 12,609.4 & 151,813.0 & 0.0019 & 9165.6 & 3291.4 & 153.4 \\ Minorities Discrimination & 8133.6 & 134,362.6 & 0.0040 & 4544.2 & 2615.4 & 974.0 \\ Political Sphere & 8494.6 & 66,261.8 & 0.0018 & 3368.0 & 3935.0 & 1191.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: For each topic, network statistics averaged across semesters: size of the network in terms of nodes and edges, network density, number of users with a Pro-Trump, Anti-Trump, or Neutral leaning score. Furthermore, we have also noticed an interesting trend among all topics and semesters: Neutral users do not fall either in an EC or form a community with a Neutral majority. We further investigate such an aspect to verify if they tend to communicate prevalently with Pro-Trump or Anti-Trump users. We found that both in minorities discrimination and Political Sphere topics, ~80% of Neutral users join Pro-Trump communities while, concerning Gun Control, they are equally distributed among opposite-side communities. Following such results, we can assume that in this case study, having a Neutral leaning score means being somewhat undecided. Figure 3: Communities evaluation for Gun Control (**a**), Minorities discrimination (**b**), and Political Sphere (**c**) topics. The scatter plots display, for each semester, the Conductance (\(x\)-axis) and Purity (\(y\)-axis) scores for each detected community.