## 3 Materials and Methods
### Multilayer Network Features  
Next, we select a set of local network measures: degree (in/out), strength (in/out), eigenvector centrality (in/out), Katz centrality (in/out), average clustering coefficient and number of communities. In general, local network measures are based on the number of node links, node position within the network, and relationship with other nodes. These are centrality measures, and they help in identification of the most influential individuals (nodes) in the network. These measures can give an insight into how nodes communicate with each other, which nodes are the most popular (hubs), how close are nodes with each other, and which nodes control the network (in terms of information flow). In the context of retweeting prediction, node centrality measures can exhibit the nodes with the largest potential to be retweeted. It is important to emphasize that the appropriate usage of centrality measures depends on the understanding of the type of links in the network and network flow [44]. Degree centrality of a node is the measure that takes into account the total number of links incident with a node. In the context of Twitter network, degree centrality can be interpreted as node with the largest number of followers or friends. However, if we capture more than one layer, degree centrality may also indicate the node with the largest number of mentions or replies. A higher degree implies popularity, and a higher possibility to gain information that is flowing through the network. According to [45], for a node \(i\) and the number of its links to other nodes \(k_{i}\), degree centrality is usually normalized by dividing it by the maximum possible degree \(N-1\):  
\[dc_{i}=\frac{k_{i}}{N-1}. \tag{4}\]  
Figure 1: Twitter represented via multilayer network. Communication on Twitter captured via four layers of multilayer network: \(G^{1}\), tweet layer; \(G^{2}\), follower layer; \(G^{3}\), reply layer; and \(G^{4}\), mention layer. The interconnections between nodes of the tweet layer and the follower layer are established if the user (node) from \(G^{2}\) posts a tweet (node) from \(G^{1}\). Other interlayer links are not represented in this figure due to the better visibility; however, \(G^{2}\), \(G^{3}\) and \(G^{4}\) are connected as multiplex network as explained in the text above. In weighted networks, a weighted degree is refereed to as node strength. Strength of a node \(i\) is defined as the sum of all weights attached to links belonging to this node [45]:  
\[s_{i}=\sum_{j\in\Pi(i)}w_{ij}, \tag{5}\]  
where \(\Pi(i)\) denotes the set of neighbouring nodes of a node \(i\). Eigenvector centrality is introduced by [PERSON] [46]. It takes into account the centrality of the adjacent nodes. It can be interpreted as a measure of influence of a node in a network. A high eigenvector score means that a node is connected to many nodes that themselves have high scores. Relative scores are assigned to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score than equal connections to low-scoring nodes. For the node \(i\) and constant \(\lambda\) centrality \(ce_{i}\) of node \(i\) is defined as [46]:  
\[ce_{i}=\frac{1}{\lambda}\sum_{j\in\Pi(i)}ce_{j}. \tag{6}\]  
Eigenvector centrality computes the centrality for a node based on the centrality of its neighbors. The eigenvector centrality for node \(i\) is the \(i\)th element of the vector \(x\) defined by the equation [45]  
\[Ax=\lambda x, \tag{7}\]  
where \(A\) is the adjacency matrix of graph \(G\) with eigenvalues \(\lambda\). There is a unique solution \(x\), all of whose entries are positive, if \(\lambda\) is the largest eigenvalue of the adjacency matrix [45]. For directed graphs, Equation (6) calculates the \"left\" eigenvector centrality which corresponds to the in-edges in the graph. For calculating out-edges' eigenvector centrality, it is necessary to reverse the graph \(G\).