# Immigration as a Divisive Topic: Clusters and Content Diffusion in the Italian Twitter Debate
## 3 Methods and Results
### How Do They Interact? Analysis of the RT Network  
In order to understand how interactions and communications unfold among users, we adopt a network analysis approach. We can build at least three different networks, one for each type of Twitter interaction: a retweet (RT) network (which includes quotes), a reply_to network and a mention network. In particular:  
* **RT network**: each node is a Twitter user, and a link is established between two nodes if one of the users retweets or quotes the other. The link is weighted, with the weight representing the number of RTs and quotes between the two users. * **Reply network**: each node is a Twitter user, and a link is established between two nodes if one of the users replies to the other. Here as well, the weight is the number of replies between the two. * **Mention network**: each node is a Twitter user, and a link is established between two nodes if one of the users mentions the other. The same weighting mechanism applies to this network. Each network is weighted based on the number of repeated interactions between the same pair of nodes. Other basic statistics on the networks are displayed in Table 3.  
For the purpose of the community detection, since we are using the Louvain algorithm, we consider the networks as undirected. For other measures, we will keep the directions into account. The present work is focused on the RT (Retweet) network, since retweets are the vast majority of events in our dataset. In addition, we want to focus on structural characteristics that are shaped according to a clear homophily principle, in order to detect graph clusters made of users that are more likely to share same viewpoint. Empirical studies have proven that a retweet between two users is more likely to be interpreted as endorsement [8; 9; 11], whereas'reply to' or'mention' can also manifest disagreement. Particularly, we concentrate on the largest connected component in the RT network which contains 97.9% of the nodes. In order to assess the presence of assortativity in the RT network, we compute the average nearest neighbour degree [32], whose results are shown in Figure 3a. We find a slightly disassortive behaviour further confirmed by the comparison with a null model obtained with a degree-preserving randomisation of our network through a configuration model (see Figure 3b). Hence, we have that lower degree nodes (i.e., ordinary citizens) are very likely to retweet messages produced by high-degree nodes (i.e., account associated to very popular persons). \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **RT Network** & **Reply Network** & **Mention Network** \\ \hline
**Number of nodes** & 232,384 & 75,319 & 130,202 \\
**Number of links** & 2,210,242 & 280,318 & 770,505 \\
**Density** & \(8\times 10^{-5}\) & \(1\times 10^{-4}\) & \(9\times 10^{-4}\) \\
**Size of Giant Component** & 227,597 & 75,319 & 130,202 \\
**Modularity** & 0.48 & 0.44 & 0.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Basic statistics of the migration debate Twitter networks. By ranking the nodes according to their degree centrality, we find that the most central nodes with respect to the degree can all be traced back to news media, journalists and politicians (Table 4). This is not entirely unexpected, given the very nature of the system under examination; the identity and the role of opinion leaders in political debates on Twitter has already been studied in scientific literature [33]. More in general, the nodes with the highest degree, i.e., those driving the debate, represent those same public actors that might fuel the offline debate, while the \"common citizens\" remain more on the sidelines, often limiting themselves to a passive engagement in content sharing rather then being proactive.