The proposed research on pre-training temporal graph neural networks across multiple networks has the potential to advance the field of machine learning and its applications significantly. By introducing methodologies to enhance the scalability and transferability of TGNNs, this work could revolutionize areas like network security, financial fraud detection, and real-time social network analysis, where dynamic and adaptive models are essential. The publicly available dataset of 84 Ethereum-based temporal networks will serve as a valuable resource for the research community, fostering innovation and collaboration. Furthermore, the principles of multi-network pre-training introduced here can inspire analogous advances in other temporal data domains, such as healthcare, transportation, and climate science. This research opens up a new direction in training generalizable temporal graph models that, for the first time, can be trained on distinct temporal networks, paving the way for Temporal Graph Foundation Models. This work also introduces a set of Ethereum transaction token networks, which are publicly available to users who have the necessary resources, such as fast SSDs, large RAM, and ample disk space, to synchronize Ethereum clients and manually extract blocks. Additionally, all Ethereum data is accessible on numerous Ethereum explorer sites such as etherscan.io. An Ethereum user's privacy depends on whether personally identifiable information (PII) is associated with any of their blockchain address, which serves as account handles and are considered pseudonymous. If such PII were obtained from other sources, our datasets could potentially be used to link Ethereum addresses. However, real-life identities can only be discovered using IP tracking information, which we neither have nor share. Our data does not contain any PII. Furthermore, we have developed a request to exclude an address from the dataset. Benchmark datasets have become fundamental for advancing graph machine learning, providing a common ground to evaluate models and facilitate the development of graph foundation models. Early graph ML studies often relied on a handful of small, static benchmark graphs (e.g., citation networks like Cora/Citeseer and molecular graphs from the TU collection [37]).

Temporal Graph Learning (TGL) aims to discover patterns in evolving networks or temporal graphs and leverage these patterns to predict future interactions. However, most existing research focuses on learning from a single network in isolation, leaving the challenges of within-domain and cross-domain generalization largely unaddressed. In this study, we introduce a new benchmark of 84 real-world temporal transaction networks and propose Temporal Multi-network Transfer (MiNT), a pre-training framework designed to capture transferable temporal dynamics across diverse networks. We train MiNT models on up to 64 transaction networks and evaluate their generalization ability on 20 held-out, unseen networks. Our results show that MiNT consistently outperforms individually trained models, revealing a strong relation between the number of pre-training networks and transfer performance. These findings highlight scaling trends in temporal graph learning and underscore the importance of network diversity in improving generalization. This work establishes the first large-scale benchmark for studying transferability in TGL and lays the groundwork for developing Temporal Graph Foundation Models.

Dynamic graph modeling aims to uncover evolutionary patterns in real-world systems, enabling accurate social recommendation and early detection of cancer cells. Inspired by the success of recent state space models in efficiently capturing long-term dependencies, we propose DyG-Mamba by translating dynamic graph modeling into a long-term sequence modeling problem. Specifically, inspired by Ebbinghaus' forgetting curve, we treat the irregular timespans between events as control signals, allowing DyG-Mamba to dynamically adjust the forgetting of historical information. This mechanism ensures effective usage of irregular timespans, thereby improving both model effectiveness and inductive capability. In addition, inspired by Ebbinghaus' review cycle, we redefine core parameters to ensure that DyG-Mamba selectively reviews historical information and filters out noisy inputs, further enhancing the model's robustness. Through exhaustive experiments on 12 datasets covering dynamic link prediction and node classification tasks, we show that DyG-Mamba achieves state-of-the-art performance on most datasets, while demonstrating significantly improved computational and memory efficiency.

For communication-efficient decentralized learning, it is essential to employ dynamic graphs designed to improve the expected spectral gap by reducing deviations from global averaging. The 1-peer exponential graph demonstrates its finite-time convergence property-achieved by maximizing the expected spectral gap-but only when the number of nodes n is a power of two. However, its efficiency across any nand the commutativity of mixing matrices remain unexplored. We delve into the principles underlying the 1-peer exponential graph to explain its efficiency across any nand leverage them to develop new dynamic graphs. We propose two new dynamic graphs: the k-peer exponential graph and the nullcascade graph. Notably, the null-cascade graph achieves finite-time convergence for any nwhile ensuring commutativity. Our experiments confirm the effectiveness of these new graphs, particularly the null-cascade graph, in most test settings.

Dynamic Bayesian networks (DBNs) are a widely used framework for modeling systems whose probabilistic structure evolves over time. Standard inference methods focus on local conditional distributions and can miss larger-scale patterns in how dependencies between variables organize and change over time. We introduce a topological approach to this problem. To each DBN we associate a time-varying graph, called a Dynamic Bayesian Graph (DBG), by assigning to each edge a strength that measures variation in its conditional dependence across parent configurations, and retaining edges whose strength exceeds a chosen threshold. We show that this construction fits within the dynamic graph framework of Kim and Mémoli, enabling the use of tools from topological data analysis. Applying persistent homology to a DBG produces a barcode, which records the merging and disappearance of connected groups of strongly dependent variables over time. We prove that this barcode is stable: small perturbations in the conditional probability tables of the DBN lead to small changes in the resulting barcode. This yields a principled and noise-resistant summary of how dependency structure evolves in a dynamic Bayesian network.

Despite the prevalence of recent success in learning from static graphs, learning from time-evolving graphs remains an open challenge. In this work, we design new, more stringent evaluation procedures for link prediction specific to dynamic graphs, which reflect real-world considerations, to better compare the strengths and weaknesses of methods. First, we create two visualization techniques to understand the reoccurring patterns of edges over time and show that many edges reoccur at later time steps. Based on this observation, we propose a pure memorization-based baseline called EdgeBank. EdgeBank achieves surprisingly strong performance across multiple settings which highlights that the negative edges used in the current evaluation are easy. To sample more challenging negative edges, we introduce two novel negative sampling strategies that improve robustness and better match real-world applications. Lastly, we introduce six new dynamic graph datasets from a diverse set of domains missing from current benchmarks, providing new challenges and opportunities for future research. Our code repository is accessible at https://github.com/fpour/DGB.git.

For brevity, we denote the SBM model as SBM(pin,pout), where pin [0,1]C 1 and pout denotes the link probability between the nodes belonging to the same class and the link probability between the nodes from different classes respectively. We adopt C = 5 classes. Based on the class label, each node has two types of parameters flow {0.02,0.04,0.08,0.10,0.12}and

Dynamic graph neural networks (DyGNNs) currently struggle with handling distribution shifts that are inherent in dynamic graphs. Existing work on DyGNNs with out-of-distribution settings only focuses on the time domain, failing to handle cases involving distribution shifts in the spectral domain. In this paper, we discover that there exist cases with distribution shifts unobservable in the time domain while observable in the spectral domain, and propose to study distribution shifts on dynamic graphs in the spectral domain for the first time. However, this investigation poses two key challenges: i) it is non-trivial to capture different graph patterns that are driven by various frequency components entangled in the spectral domain; and ii) it remains unclear how to handle distribution shifts with the discovered spectral patterns. To address these challenges, we propose Spectral Invariant Learning for Dynamic Graphs under Distribution Shifts (SILD), which can handle distribution shifts on dynamic graphs by capturing and utilizing invariant and variant spectral patterns. Specifically, we first design a DyGNN with Fourier transform to obtain the ego-graph trajectory spectrums, allowing the mixed dynamic graph patterns to be transformed into separate frequency components. We then develop a disentangled spectrum mask to filter graph dynamics from various frequency components and discover the invariant and variant spectral patterns. Finally, we propose invariant spectral filtering, which encourages the model to rely on invariant patterns for generalization under distribution shifts. Experimental results on synthetic and real-world dynamic graph datasets demonstrate the superiority of our method for both node classification and link prediction tasks under distribution shifts.