# Evolutionary Features for Dynamic Link Prediction in Social Networks
## 2 Dynamic Similarity Metrics
### Actor-Level Evolution in a Dynamic Network  
As mentioned earlier, a dynamic network can be defined as a temporal sequence of small-scale network snapshots where each snapshot is known as a short-interval network (SIN). Actors experience variances in their link structure, altering neighbourhoods and subsequently changing network positions over time. The increasing size and complexity of modern dynamic networks have instigated the mechanism of splitting a large network into small-scale manageable components that facilitate the visualization and inference procedure. It simplifies the expedition of different aspects of the network to describe it succinctly without computational difficulties. Modifications of actors' network positions in SINs over time due to the varying nature of performing network activities (i.e., link formation, link deletion) and changing neighbourhoods are visualized in Figure 1. The top row in this figure represents a time series of three network snapshots \(G_{1}\), \(G_{2}\), \(G_{3}\), known as short-interval networks (SIN), where these evolutionary networks are analysed to predict a future link between actor \(a_{1}\) and \(a_{2}\) at timestamp \(t=4\) in \(G_{4}\). The bottom row represents the aggregated networks at timestamps \(t=2,3\) where the first network denotes a union of \(G_{1}\), \(G_{2}\) (i.e.,\(G_{1}\cup G_{2}\)), and the second one denotes a union of \(G_{2}\), \(G_{3}\) (i.e., \(G_{2}\cup G_{3}\)). Each network snapshot is accompanied by three centrality measures (i.e., degree, closeness, and betweenness) and neighbourhood incident to actor \(a_{1}\) and \(a_{2}\) at different timestamps both in individual short-interval networks and in aggregated networks. In the top row of this figure, the link structure and neighbourhoods of two actors (i.e., \(a_{1}\) and \(a_{2}\)) are portrayed in three different SINs at three different timestamps (i.e., \(t_{1}\), \(t_{2}\) and \(t_{3}\)). The numbers on top of each SIN segment denote three different centrality measures (i.e., degree, closeness, and betweenness) for these two actors, and at the bottom of these three SINs, the neighbouring actors of these two actors are presented. Three centrality measures were computed using the networkX [39] package that supports the exploration and analysis of networks and network algorithms. For example, according to networkX, the degree centrality of an actor is the fraction of nodes it is connected to, and the closeness of an actor is the reciprocal of the average shortest path distance to that actor over other \(n-1\) reachable nodes by considering \(n\) number of actors in the network. It is observable that the varying network positions of actors in temporal networks can be mapped by the centrality measures effectively. For example, actor \(a_{2}\) experienced a higher degree and closeness centrality in comparison to \(a_{1}\) in SIN \(G_{1}\), whereas actor \(a_{1}\) achieved a higher measure value in SIN \(G_{2}\) in comparison to \(a_{2}\). Conversely, although both achieved a similar degree centrality in SIN \(G_{3}\), their closeness and betweenness centrality measures vary according to their network positions. Likewise, actor \(a_{1}\) gained a new neighbourhood in \(G_{2}\) which is different from what it had in \(G_{1}\). Furthermore, in \(G_{3}\), it regained one of its previous neighbourhoods (i.e., \(a_{6}\)). Simultaneously, despite its retention of previously gained neighbors (i.e., \(a_{6}\)) in \(G_{3}\), it lost one of its neighbors from \(G_{2}\) (i.e., \(a_{8}\)). Similar observations are evident in the case of actor \(a_{2}\). Therefore, it is believed that actors experience variable changes in their network positions and neighbourhoods due to micro-level network activities.