# Exploring the Performance of Continuous-Time Dynamic Link Prediction Algorithms
## 2 Related Work  
**Temporal Networks**. Temporal networks have been utilized to model extensive systems that comprise entities interacting over time (see [PERSON] and [PERSON] [7] and [PERSON] and [PERSON] [17] for a general introduction). As highlighted by [PERSON] and [PERSON] [18], temporal networks have been studied under different terminologies, including dynamic/temporal graphs/networks, depending on the task and the way time is modeled. In particular, some works consider time as discrete [19] and others as continuous [20]. In the present paper, we consider Continuous-Time Dynamic Graphs, as defined in [8; 21], and the representation used is the \"sequence of interaction model of temporal networks\" [18]. The emphasis is on predicting the events on different time intervals, and not on studying emergent properties. Although our focus is on continuous-time graphs, the methodology proposed in this paper applies to both discrete and continuous-time representations. **Visualizing Temporal Networks**. Due to the additional complexity introduced by the time dimension, visualizing temporal graphs faces unique challenges, as discussed in recent surveys [22]. As detailed by [PERSON] et al. [23], the time aspect exacerbates visual clutter issues, which are already common in static network visualization. They propose node activity maps, a method to visualize node activity over time, but do not consider the evaluation of Dynamic Link Prediction as a use case. Temporal edge traffic (TET) and Temporal edge activity (TEA) plots proposed by [PERSON] et al. [8] enable the understanding of the effect of time-based splitting on the edges. However, as these visualizations focus on visualizing the events directly, edges that are exclusively observed in the training set are represented in the region as those observed both in the train and test sets, rendering a visual comparison of these two sets difficult. In contrast, our proposed Birth-Death diagram focuses on directly illustrating the division of nodes and edges into three distinct regions. Figure 1: A Birth–Death diagram on a recording of face-to-face interactions among high school students over 9 days [16]. The y and x coordinates for each node/edge represent their first (Birth) and last (Death) interaction time, respectively. Given a cutoff time \(t_{split}\), while the history of interaction is divided into a train or a test set, the nodes and edges are partitioned into three categories: historical, overlap, and inductive. The surprise index is the ratio \(\frac{Indictive+Overlap}{Indictive+Overlap}\). Methods for DLP. (Dynamic) Link Prediction is a longstanding problem, and various classes of methods have been proposed to address it. Early efforts focused on using traditional tools from statistics and network science, often borrowing from the existing literature on the modeling of static networks. These include univariate time series models [24; 25], similarity-based methods [26], probabilistic generative models [27; 28; 29; 30], and matrix and tensor factorization [31]. Nevertheless, with the success of deep learning and representation learning on static graphs, recent approaches have shifted towards using neural networks, as surveyed by [PERSON] et al. [9] and [PERSON] et al. [10]. Notably, _memory-based_ dynamic graph neural networks (DGNNs) such as TGN [21] and DyRep [32], use an encoder-decoder architecture. The encoder maps each node to a time-varying representation in a low-dimensional space, while the decoder allows for calculating the probability of interactions from the latent representations of the nodes. More generally, the idea of learning a vector representation (embedding), either at the node level or the edge level, has been explored in several other papers [33; 34; 35; 36; 37; 38]. It is important to consider that there is currently a lack of fair and objective comparison between these embedding-based techniques and shallow methods such as the ones previously detailed.