A generative model for temporal networks that jointly controls community evolution and dynamic node sets and is used as a benchmark to study the impact of the rate at which nodes join/leave the network on the performance of dynamic community detection algorithms.
Abstract
This paper introduces a generative model for temporal networks that jointly controls community evolution and dynamic node sets. The model represents community structure as a sequence of partitions and uses a genetic search guided by a similarity measure based on mutual information to regulate changes between snapshots. This allows explicit control of community evolution including splits and merges while handling node additions and removals. Temporal edges are then generated using intra- and inter-community probabilities derived from data or theoretical bounds to ensure connectivity. Simulation experiments on real-world datasets demonstrate the ability of the generative model to model the evolution of real dynamic communities. The model is used as a benchmark to study the impact of the rate at which nodes join/leave the network on the performance of dynamic community detection algorithms.
By specifying a stochastically evolving hidden Markov network model, this work addresses two important directions for further investigation identified by Chang et al. (2022): robustness to non-identical network replicates, and efficient aggregation of multiple available network snapshots.
Understanding how links form and predicting future link states is of great importance in social, traffic, and many other complex temporal networks. These temporal networks are typically governed by multiple evolutionary mechanisms. However, existing dynamic graph representation methods, especially dynamic graph neural networks (DGNNs), are constrained by their single-evolutionary-path architecture, where spatial and temporal dynamics are either sequentially stacked or integrated into a monolithic module in a fixed manner. This design not only restricts the exploration of diverse evolutionary paths arising from rich evolutionary mechanisms but also confines spatiotemporal interactions to passive and implicit modeling, resulting in compromised performance and weak interpretability. To address these issues, we propose a novel theoretical model, namely the multiway autoregressive (MARS) model, which characterizes multiple evolutionary paths by capturing dependencies within and across two core factors underlying diverse evolutionary mechanisms. Based on this theoretical foundation, we develop a general DGNN framework, a multiway autoregressive network (MAN), by transforming the network architecture into a 2-D diagram that characterizes evolutionary dependencies in the spatiotemporal domain. Each node encodes an evolving state of the dynamic graph representation, while each edge denotes an evolutionary transition from one state to another. Moreover, three elementary evolutionary operators are incorporated into edges along distinct directions, capturing spatialwise, temporalwise, and cross-spatiotemporal evolutionary dynamics, respectively. This enables researchers to develop a variety of DGNNs by configuring the evolutionary operators in different ways. To validate the effectiveness of this framework, we design a new DGNN, which employs a graph convolutional network (GCN), a gated recurrent unit (GRU), and our proposed time-delayed GCN (TD-GCN) as core components. Promising experimental results demonstrate that the proposed approach achieves state-of-the-art temporal link prediction performance on both synthetic and real-world temporal networks across diverse domains.
Ping He, Xiao-hua Xu· IEEE Transactions on Neural...· 0 citations
Dynamic community detection on temporal graphs seeks to identify evolving community structures while allowing node memberships to change over time. In this work, we formulate dynamic community detection over observed node-time instances, where each node-time instance in the temporal interaction stream is assigned a cluster label. We propose a diffusion-guided contrastive learning framework that uses a local temporal diffusion affinity matrix to construct positive and negative node-time pairs and organise the learned representations according to their temporal structural relationships. We then apply a clustering algorithm to the resulting embedding space to detect dynamic communities. Experiments on synthetic temporal networks show that the proposed method outperforms static community detection baselines and achieves competitive or better performance than existing dynamic community detection methods in terms of AMI and ARI, while maintaining good scalability. We further apply the method to a large-scale OpenAlex computer science collaboration network from 2016 to 2025, revealing persistent and evolving collaboration communities in real scientific data. These results suggest that time-node-level representation learning provides an effective framework for scalable dynamic community detection on temporal graphs.
Pei-Jie Zhong, Raúl Mondragón, Richard Clegg· 0 citations
In many research fields, there is an increased availability of network data arising as replicated networks. However, most statistical models for network data in the literature are designed for a single network. Among these, the Stochastic Block Model is arguably the most popular model to perform vertex clustering and community detection. We propose the Hierarchical Stochastic Block Model, a generalization of the SBM to the setting of replicated networks. This model uses a Hierarchical Pitman-Yor prior for the block allocation vector of each graph, and allows different networks to share the same latent blocks. The number of blocks in each graph and the overall number of blocks need not be specify by the practitioner, hence avoiding complicated model selection procedures. A novel MCMC algorithm to perform posterior inference is derived. To illustrate how the model is able to capture different levels of block sharing, the HSBM is fit to a co-authorship and a brain connectomic network.
Marco Battiston, Clement Lee· Statistics and computing· 0 citations
Temporal graphs are increasingly used to model dynamic systems in diverse domains such as social networks, financial networks, and traffic networks. Predicting both what the next event will be and when it will occur in these systems is crucial for understanding and anticipating complex behaviors, but has not been studied much. To address this gap, we propose a unified mathematical framework capable of capturing varying degrees of complexity across temporal graphs. Our framework is flexible and expressive enough to accommodate a wide range of network structures and temporal dynamics. Building upon this analysis, we introduce our novel approach for jointly predicting the next event and its occurrence time. Empirical evaluations across multiple datasets demonstrate that our method consistently outperforms existing techniques, particularly in scenarios involving irregular event patterns and complex temporal dependencies. These findings highlight the potential of our framework as a robust foundation for future research in temporal event prediction.
Mohammad Ostadmohammadi, Sepehr Kazemi, Hamid R. Rabiee· 0 citations
The framework gives a nonparametric baseline for dynamic network analysis with explicit convergence guarantees and establishes nonparametric convergence rates in both block-model and Holder-smooth regimes.
