## 2 Related Work  
In recent years, Graph Neural Networks (GNNs) have been applied to a wide range of problems [11]. Utilizing graphs as a data structure provides valuable insights by analyzing the interactions between its elements (vertices and edges). With the integration of neural networks, processing these interactions can be achieved by incorporating techniques such as message passing [12], attention mechanisms [13], heterogeneity [14], or the temporal dynamics of the graph [15], among others. The temporal dimension is crucial for capturing the interactions between various entities within a graph. Temporal graphs introduce an additional layer of information that can be examined through a discrete or continuous perspective. Graph Neural Networks designed for discrete and continuous time graphs leverage this temporal data and have been applied to address a range of challenges [16; 17; 18]. The temporal dependencies within a graph are vital for many processes [9; 19], as they can enhance the accuracy of classification or prediction tasks involving vertices, edges, or entire graphs by incorporating these temporal details. By leveraging Graph Neural Networks, the structural information of graphs can be utilized for fraud prediction on online platforms [3; 5], as fraudulent activities often tend to cluster due to network homophily (the tendency for individuals to form small, homogeneous groups). Recently, there has been an increasing interest in applying these methods to real-world operational data, primarily because access to such information has traditionally been limited. A new approach involves using Graph Neural Networks (GNNs) for fraud detection. The central premise is that fraud can be represented as a graph or network where various entities interact. Additionally, homophily can be relevant in this context, as fraud often exhibits clustering behavior. Moreover, the increasing interest in using GNNs with dynamic graphs has led to their application in detecting fraudulent activities. For instance, [5] explores dynamic homogeneous graphs within a transactional graph segmented into temporal snapshots. This approach employs a GNN message-passing module, attention mechanisms, and convolutional aggregation within each temporal snapshot. Processing data as a temporal sequence of graphs enables classifying fraudulent transactions. Other studies have similarly focused on utilizing temporal snapshots to identify fraudulent accounts and transactions [7]. This approach involves creating temporal and structural graphs processed through multiple layers of a Graph Convolutional Network (GCN). The timestamp information, which indicates when an event occurs, is combined with the vertex features, and the representation of two connected vertices is derived from the product of their embeddings (a transformation that maps from a high-dimensional space, like a graph, to a lower-dimensional space, like a vectorial space). Likewise, [20] adopts a structural and temporal approach, generating embeddings for connected vertices and their temporal relationships by chaining convolutional layers of both the structural and temporal graphs. This method is applied to detect large-scale fraudulent account registrations. In [21], a heterogeneous dynamic graph detects fraudulent transactions. It uses three types of graphs (static, instantaneous temporal, and two-stage directed) obtained from transaction logs. The static and instantaneous graphs construct the two-stage directed graph used in the training and inference. The training combines a GCN (Graph Convolutional Network) layer for the batch graph (historical part of the two-stage directed graph) and a GCN layer for the real-time graph (current entities and transactions). The contribution of [21] is that the results of the batch graph are stored in a database. In this way, training and inference reduce the latency times of traditional methods. The previous works have primarily concentrated on discrete temporal graph applications, with limited attention given to the continuous aspect.