# Evolutionary Features for Dynamic Link Prediction in Social Networks
## 2 Dynamic Similarity Metrics
### Actor-Level Evolution in a Dynamic Network
#### 2.1.1 Structural Dynamicity  
The change in link structure and network positions experienced by actors in every SIN over time can be measured using different network measures utilized in social network analysis [38]. Therefore, this study used the following composite measure to quantify an actor's structural position in a network snapshot:  
\[C_{t}^{a}=\left\{ \begin{matrix}deg_{a}(G_{t})+cls_{a}(G_{t})+btwn_{a}(G_{t})&a \in V_{t}\\ 0&a\
otin V_{t}\end{matrix} \right. \tag{1}\]  
where \(C_{t}^{a}\) denotes network status/position of actor \(a\) in a SIN, \(G_{t}(V_{t},E_{t})\) at time \(t\); \(deg_{a}(G_{t})\), \(cls_{a}(G_{t})\), and \(btwn_{a}(G_{t})\) denote the degree, closeness and betweenness centrality of actor \(a\) in \(G_{t}\). The underlying reasons for using a composite measure as a combination of three centrality measures are, firstly, that these measures are well-defined and can successfully quantify an actor's connectivity, position, communication dynamics, influence and broadcasting capabilities, and importance in a network, and, secondly, that these measures are correlated. For example, an actor with high betweenness and low closeness centrality can monopolize links from a small number of actors to many others. Likewise, a high degree with low closeness centrality denotes that the actor is embedded in a cluster far from the rest of the network. It is noteworthy that, in the case of a directed network, \(deg_{a}(G_{t})\) can be either in-degree or out-degree centrality measures of actors, or it can be a combination of both. This study considered the aggregation of in-degree and out-degree centrality measures together. Motivated by the perception of these actor-oriented dynamic changes, the concept of an actor's positional dynamicity was developed by [PERSON] et al. [38] to quantify the temporal variations considering both dynamic and static social network topology. The underlying reason is that, according to social network topology, a dynamic network needs to be analysed in regard to the temporal aggregation of links among its actors [40], and simultaneously, different aspects of the dynamicity of dynamic networks can be quantified using both static and dynamic topology of social network analysis [41]. Furthermore, [PERSON] et al. [42] used local topological similarity indices (e.g., AdamicAdar, Jaccard Coefficient), and unlike other supervised dynamic link prediction methods ([34,36]), instead of building time series of these indices, they considered their variations between adjacent  
Figure 1: Visualisation of a dynamic link prediction framework considering a series of evolutionary network snapshots at different discrete timestamps (\(t=1,2,3,4\)) using abstract data. time steps. To find out the intrinsic relationship between the structural variations and the formation of links between non-connected actor pairs, the authors also defined a measure to quantify the rate of change of the structural properties. Following that, this study defined structural dynamicity as the rate or degree of actor-level structural changes computed at time \(t\) using the following equation:  
\[\delta^{a}(t)=\frac{C_{t}^{a}-C_{t-1}^{a}}{C_{t,t-1}^{a}} \tag{2}\]  
where \(\delta^{a}(t)\) denotes the rate of structural dynamicity demonstrated by an actor \(a\) at timestamp \(t\). \(C_{t}^{a}\) denotes the composite centrality measure, defined in Equation (1), incident to actor \(a\) in a network snapshot \(G_{t}\) at time \(t\), whereas \(C_{t-1}^{a}\) denotes the same centrality measure incident to actor \(a\) in a network snapshot at time \(t-1\) (i.e., previous timestamp) and finally, \(C_{t,t-1}^{a}\) denotes the same measure of actor \(a\) in an aggregated network \(G_{t}\cup G_{t-1}\). This basically quantifies the structural and/or topological changes of every actor that it experiences at every timestamp in temporal networks.