Recent advancements in graph representation learning have shifted attention towards dynamic graphs, which exhibit evolving topologies and features over time. The increased use of such graphs creates a paramount need for generative models suitable for applications such as data augmentation, obfuscation, and anomaly detection. However, there are few generative techniques that handle continuously changing temporal graph data; existing work largely relies on augmenting static graphs with additional temporal information to model dynamic interactions between nodes. In this work, we propose a fundamentally different approach: We instead directly model interactions as a joint probability of an edge forming between two nodes at a given time. This allows us to autoregressively generate new synthetic dynamic graphs in a largely assumption free, scalable, and inductive manner. We formalize this approach as DG-Gen, a generative framework for continuous time dynamic graphs, and demonstrate its effectiveness over five datasets. Our experiments demonstrate that DG-Gen not only generates higher fidelity graphs compared to traditional methods but also significantly advances link prediction tasks.

Deep generative models have recently achieved significant success in modeling graph data, including dynamic graphs, where topology and features evolve over time. However, unlike in vision and natural language domains, evaluating generative models for dynamic graphs is challenging due to the difficulty of visualizing their output, making quantitative metrics essential. In this work, we develop a new quality metric for evaluating generative models of dynamic graphs. Current metrics for dynamic graphs typically involve discretizing the continuous-evolution of graphs into static snapshots and then applying conventional graph similarity measures. This approach has several limitations: (a) it models temporally related events as i.i.d. samples, failing to capture the non-uniform evolution of dynamic graphs; (b) it lacks a unified measure that is sensitive to both features and topology; (c) it fails to provide a scalar metric, requiring multiple metrics without clear superiority; and (d) it requires explicitly instantiating each static snapshot, leading to impractical runtime demands that hinder evaluation at scale. We propose a novel metric based on the Johnson-Lindenstrauss lemma, applying random projections directly to dynamic graph data. This results in an expressive, scalar, and application-agnostic measure of dynamic graph similarity that overcomes the limitations of traditional methods. We also provide a comprehensive empirical evaluation of metrics for continuous-time dynamic graphs, demonstrating the effectiveness of our approach compared to existing methods. Our implementation is available at https://github.com/ryienh/jl-metric.

Graph Neural Networks learn on graph-structured data by iteratively aggregating local neighborhood information. While this local message passing paradigm imparts a powerful inductive bias and exploits graph sparsity, it also yields three key challenges: (i) oversquashing of long-range information, (ii) oversmoothing of node representations, and (iii) limited expressive power. In this work we inject randomized global embeddings of node features, which we term Sketched Random Features, into standard GNNs, enabling them to efficiently capture long-range dependencies. The embeddings are unique, distance-sensitive, and topology-agnostic---properties which we analytically and empirically show alleviate the aforementioned limitations when injected into GNNs. Experimental results on real-world graph learning tasks confirm that this strategy consistently improves performance over baseline GNNs, offering both a standalone solution and a complementary enhancement to existing techniques such as graph positional encodings.