Recent studies successfully learned static graph embeddings that are structurally fair by preventing the effectiveness disparity of high- and low-degree vertex groups in downstream graph mining tasks. However, achieving structure fairness in dynamic graph embedding remains an open problem. Neglecting degree changes in dynamic graphs will significantly impair embedding effectiveness without notably improving structure fairness. This is because the embedding performance of high-degree and low-to-high-degree vertices will significantly drop close to the generally poorer embedding performance of most slightly changed vertices in the long-tail part of the power-law distribution. We first identify biased structural evolutions in a dynamic graph based on the evolving trend of vertex degree and then propose FairDGE, the first structurally Fair Dynamic Graph Embedding algorithm. FairDGE learns biased structural evolutions by jointly embedding the connection changes among vertices and the long-short-term evolutionary trend of vertex degrees. Furthermore, a novel dual debiasing approach is devised to encode fair embeddings contrastively, customizing debiasing strategies for different biased structural evolutions. This innovative debiasing strategy breaks the effectiveness bottleneck of embeddings without notable fairness loss. Extensive experiments demonstrate that FairDGE achieves simultaneous improvement in the effectiveness and fairness of embeddings.
Dynamic text-attributed graphs (DyTAGs) are prevalent in various real-world scenarios, where each node and edge are associated with text descriptions, and both the graph structure and text descriptions evolve over time. Despite their broad applicability, there is a notable scarcity of benchmark datasets tailored to DyTAGs, which hinders the potential advancement in many research fields. To address this gap, we introduce Dynamic Text-attributed Graph Benchmark (DTGB), a collection of large-scale, time-evolving graphs from diverse domains, with nodes and edges enriched by dynamically changing text attributes and categories. To facilitate the use of DTGB, we design standardized evaluation procedures based on four real-world use cases: future link prediction, destination node retrieval, edge classification, and textual relation generation. These tasks require models to understand both dynamic graph structures and natural language, highlighting the unique challenges posed by DyTAGs. Moreover, we conduct extensive benchmark experiments on DTGB, evaluating 7 popular dynamic graph learning algorithms and their variants of adapting to text attributes with LLM embeddings, along with 6 powerful large language models (LLMs). Our results show the limitations of existing models in handling DyTAGs. Our analysis also demonstrates the utility of DTGB in investigating the incorporation of structural and textual dynamics. The proposed DTGB fosters research on DyTAGs and their broad applications. It offers a comprehensive benchmark for evaluating and advancing models to handle the interplay between dynamic graph structures and natural language. The dataset and source code are available at https://github.com/zjs123/DTGB.
Dynamic graphs provide a flexible data abstraction for modelling many sorts of real-world systems, such as transport, trade, and social networks. Graph neural networks (GNNs) are powerful tools allowing for different kinds of prediction and inference on these systems, but getting a handle on uncertainty, especially in dynamic settings, is a challenging problem. In this work we propose to use a dynamic graph representation known in the tensor literature as the unfolding, to achieve valid prediction sets via conformal prediction. This representation, a simple graph, can be input to any standard GNN and does not require any modification to existing GNN architectures or conformal prediction routines. One of our key contributions is a careful mathematical consideration of the different inference scenarios which can arise in a dynamic graph modelling context. For a range of practically relevant cases, we obtain valid prediction sets with almost no assumptions, even dispensing with exchangeability. In a more challenging scenario, which we call the semi-inductive regime, we achieve valid prediction under stronger assumptions, akin to stationarity. We provide real data examples demonstrating validity, showing improved accuracy over baselines, and sign-posting different failure modes which can occur when those assumptions are violated.
Dynamic graph embedding has emerged as a very effective technique for addressing diverse temporal graph analytic tasks (i.e., link prediction, node classification, recommender systems, anomaly detection, and graph generation) in various applications. Such temporal graphs exhibit heterogeneous transient dynamics, varying time intervals, and highly evolving node features throughout their evolution. Hence, incorporating long-range dependencies from the historical graph context plays a crucial role in accurately learning their temporal dynamics. In this paper, we develop a graph embedding model with uncertainty quantification, TransformerG2G, by exploiting the advanced transformer encoder to first learn intermediate node representations from its current state ($t$) and previous context (over timestamps [$t-1, t-l$], $l$ is the length of context). Moreover, we employ two projection layers to generate lower-dimensional multivariate Gaussian distributions as each node's latent embedding at timestamp $t$. We consider diverse benchmarks with varying levels of ``novelty" as measured by the TEA (Temporal Edge Appearance) plots. Our experiments demonstrate that the proposed TransformerG2G model outperforms conventional multi-step methods and our prior work (DynG2G) in terms of both link prediction accuracy and computational efficiency, especially for high degree of novelty. Furthermore, the learned time-dependent attention weights across multiple graph snapshots reveal the development of an automatic adaptive time stepping enabled by the transformer. Importantly, by examining the attention weights, we can uncover temporal dependencies, identify influential elements, and gain insights into the complex interactions within the graph structure. For example, we identified a strong correlation between attention weights and node degree at the various stages of the graph topology evolution.
Dynamic interaction graphs have been widely adopted to model the evolution of user-item interactions over time. There are two crucial factors when modelling user preferences for link prediction in dynamic interaction graphs: 1) collaborative relationship among users and 2) user personalized interaction patterns. Existing methods often implicitly consider these two factors together, which may lead to noisy user modelling when the two factors diverge. In addition, they usually require time-consuming parameter learning with back-propagation, which is prohibitive for real-time user preference modelling. To this end, this paper proposes FreeGEM, a parameter-free dynamic graph embedding method for link prediction. Firstly, to take advantage of the collaborative relationships, we propose an incremental graph embedding engine to obtain user/item embeddings, which is an Online-Monitor-Offline architecture consisting of an Online module to approximately embed users/items over time, a Monitor module to estimate the approximation error in real time and an Offline module to calibrate the user/item embeddings when the online approximation errors exceed a threshold. Meanwhile, we integrate attribute information into the model, which enables FreeGEM to better model users belonging to some under represented groups. Secondly, we design a personalized dynamic interaction pattern modeller, which combines dynamic time decay with attention mechanism to model user short-term interests. Experimental results on two link prediction tasks show that FreeGEM can outperform the state-of-the-art methods in accuracy while achieving over 36X improvement in efficiency. All code and datasets can be found in https://github.com/FudanCISL/FreeGEM.
Dynamic graph embedding has gained great attention recently due to its capability of learning low dimensional graph representations for complex temporal graphs with high accuracy. However, recent advances mostly focus on learning node embeddings as deterministic "vectors" for static graphs yet disregarding the key graph temporal dynamics and the evolving uncertainties associated with node embedding in the latent space. In this work, we propose an efficient stochastic dynamic graph embedding method (DynG2G) that applies an inductive feed-forward encoder trained with node triplet-based contrastive loss. Every node per timestamp is encoded as a time-dependent probabilistic multivariate Gaussian distribution in the latent space, hence we can quantify the node embedding uncertainty on-the-fly. We adopted eight different benchmarks that represent diversity in size (from 96 nodes to 87,626 and from 13,398 edges to 4,870,863) and diversity in dynamics. We demonstrate via extensive experiments on these eight dynamic graph benchmarks that DynG2G achieves new state-of-the-art performance in capturing the underlying temporal node embeddings. We also demonstrate that DynG2G can predict the evolving node embedding uncertainty, which plays a crucial role in quantifying the intrinsic dimensionality of the dynamical system over time. We obtain a universal relation of the optimal embedding dimension, $L_o$, versus the effective dimensionality of uncertainty, $D_u$, and we infer that $L_o=D_u$ for all cases. This implies that the uncertainty quantification approach we employ in the DynG2G correctly captures the intrinsic dimensionality of the dynamics of such evolving graphs despite the diverse nature and composition of the graphs at each timestamp. Moreover, this $L_0 - D_u$ correlation provides a clear path to select adaptively the optimum embedding size at each timestamp by setting $L \ge D_u$.
Dynamic graphs arise in a plethora of practical scenarios such as social networks, communication networks, and financial transaction networks. Given a dynamic graph, it is fundamental and essential to learn a graph representation that is expected not only to preserve structural proximity but also jointly capture the time-evolving patterns. Recently, graph convolutional network (GCN) has been widely explored and used in non-Euclidean application domains. The main success of GCN, especially in handling dependencies and passing messages within nodes, lies in its approximation to Laplacian smoothing. As a matter of fact, this smoothing technique can not only encourage must-link node pairs to get closer but also push cannot-link pairs to shrink together, which potentially cause serious feature shrink or oversmoothing problem, especially when stacking graph convolution in multiple layers or steps. For learning time-evolving patterns, a natural solution is to preserve historical state and combine it with the current interactions to obtain the most recent representation. Then the serious feature shrink or oversmoothing problem could happen when stacking graph convolution explicitly or implicitly according to current prevalent methods, which would make nodes too similar to distinguish each other. To solve this problem in dynamic graph embedding, we analyze the shrinking properties in the node embedding space at first, and then design a simple yet versatile method, which exploits L2 feature normalization constraint to rescale all nodes to hypersphere of a unit ball so that nodes would not shrink together, and yet similar nodes can still get closer. Extensive experiments on four real-world dynamic graph datasets compared with competitive baseline models demonstrate the effectiveness of the proposed method.
Graph representation learning is a fundamental task in various applications that strives to learn low-dimensional embeddings for nodes that can preserve graph topology information. However, many existing methods focus on static graphs while ignoring evolving graph patterns. Inspired by the success of graph convolutional networks(GCNs) in static graph embedding, we propose a novel k-core based temporal graph convolutional network, the CTGCN, to learn node representations for dynamic graphs. In contrast to previous dynamic graph embedding methods, CTGCN can preserve both local connective proximity and global structural similarity while simultaneously capturing graph dynamics. In the proposed framework, the traditional graph convolution is generalized into two phases, feature transformation and feature aggregation, which gives the CTGCN more flexibility and enables the CTGCN to learn connective and structural information under the same framework. Experimental results on 7 real-world graphs demonstrate that the CTGCN outperforms existing state-of-the-art graph embedding methods in several tasks, including link prediction and structural role classification. The source code of this work can be obtained from \url{https://github.com/jhljx/CTGCN}.
Representation learning on graphs has emerged as a powerful mechanism to automate feature vector generation for downstream machine learning tasks. The advances in representation on graphs have centered on both homogeneous and heterogeneous graphs, where the latter presenting the challenges associated with multi-typed nodes and/or edges. In this paper, we consider the additional challenge of evolving graphs. We ask the question of whether the advances in representation learning for static graphs can be leveraged for dynamic graphs and how? It is important to be able to incorporate those advances to maximize the utility and generalization of methods. To that end, we propose the Framework for Incremental Learning of Dynamic Networks Embedding (FILDNE), which can utilize any existing static representation learning method for learning node embeddings, while keeping the computational costs low. FILDNE integrates the feature vectors computed using the standard methods over different timesteps into a single representation by developing a convex combination function and alignment mechanism. Experimental results on several downstream tasks, over seven real-world data sets, show that FILDNE is able to reduce memory and computational time costs while providing competitive quality measure gains with respect to the contemporary methods for representation learning on dynamic graphs.
DynamicGEM is an open-source Python library for learning node representations of dynamic graphs. It consists of state-of-the-art algorithms for defining embeddings of nodes whose connections evolve over time. The library also contains the evaluation framework for four downstream tasks on the network: graph reconstruction, static and temporal link prediction, node classification, and temporal visualization. We have implemented various metrics to evaluate the state-of-the-art methods, and examples of evolving networks from various domains. We have easy-to-use functions to call and evaluate the methods and have extensive usage documentation. Furthermore, DynamicGEM provides a template to add new algorithms with ease to facilitate further research on the topic.