Community-Aware Temporal Walks: Parameter-Free Representation Learning on Continuous-Time Dynamic Graphs

TL;DR

CTWalks addresses temporal link prediction on continuous-time dynamic graphs by integrating three core ideas: (i) a parameter-free, community-aware temporal walk sampling that distinguishes intra- and inter-community transitions; (ii) an anonymization strategy enriched with community labels to preserve structural roles while enabling generalization to unseen nodes; and (iii) a Neural ODE-based encoding that continuously models temporal dynamics alongside discrete updates. The framework reveals a theoretical connection to matrix factorization via a two-layer walk with intra- and inter-community transition matrices, and it demonstrates superior performance on multiple real-world CTDG datasets, especially in inductive settings. CTWalks thus offer a robust, scalable approach to capture mesoscopic graph structure and continuous-time dynamics for accurate temporal link prediction with strong generalization capabilities.

Abstract

Dynamic graph representation learning plays a crucial role in understanding evolving behaviors. However, existing methods often struggle with flexibility, adaptability, and the preservation of temporal and structural dynamics. To address these issues, we propose Community-aware Temporal Walks (CTWalks), a novel framework for representation learning on continuous-time dynamic graphs. CTWalks integrates three key components: a community-based parameter-free temporal walk sampling mechanism, an anonymization strategy enriched with community labels, and an encoding process that leverages continuous temporal dynamics modeled via ordinary differential equations (ODEs). This design enables precise modeling of both intra- and inter-community interactions, offering a fine-grained representation of evolving temporal patterns in continuous-time dynamic graphs. CTWalks theoretically overcomes locality bias in walks and establishes its connection to matrix factorization. Experiments on benchmark datasets demonstrate that CTWalks outperforms established methods in temporal link prediction tasks, achieving higher accuracy while maintaining robustness.

Figures (4)

• Figure 1: Traditional anonymous encodings fail to differentiate nodes with similar local structures but distinct community roles, such as $A$ and $F$. Without community context, the identical structures of $A$ and $F$ make it impossible to predict $D$’s relationship with either node.
• Figure 2: Illustration of the encoding mechanism in CTWalks. Each node in the temporal walk is processed through instantaneous updates ($g$) and continuous temporal integration ($f$) along an irregular time trajectory. The final hidden state $h_4$ represents the walk encoding, incorporating both structural and community-aware information.
• Figure 3: Illustration of the data preparation process for link prediction. The process includes sorting edges by timestamp, splitting into training, validation, and testing sets, and performing negative sampling to ensure balanced datasets.
• Figure 4: Comparison of temporal dynamics modeling approaches. Standard RNN maintains constant hidden states; RNN-Decay introduces exponential decay; Neural ODE models smooth continuous trajectories; ODE-RNN combines discrete updates with continuous dynamics.