model dynamic networks

This work addresses the challenge of modeling dynamic community evolution—encompassing community splitting, merging, and node additions or deletions—by proposing a novel generative temporal network model. The approach introduces, for the first time, a mutual information–based similarity measure to guide genetic search, thereby explicitly controlling the evolution of community structure across network snapshots. It further incorporates dynamic edge-generation probabilities conditioned on intra- and inter-community connectivity. The model jointly captures both the temporal evolution of communities and changes in node membership. Experimental results demonstrate that the framework effectively reproduces real-world dynamic community behaviors and successfully quantifies how node insertion and deletion rates influence the performance of dynamic community detection algorithms.

This work proposes a statistical inference framework based on a hidden Markov network model to accurately estimate subgraph densities and enable joint multi-timepoint comparisons for non-i.i.d. dynamic network sequences subject to observation errors. By explicitly modeling edge-wise observation noise, the method achieves, for the first time, robust inference of subgraph densities across heterogeneous network snapshots and leverages information from multiple time points to enhance estimation efficiency. Theoretical analysis demonstrates that the proposed approach enjoys favorable asymptotic properties in large-scale networks, substantially improving both accuracy and computational efficiency in inferring subgraph structures from noisy dynamic networks.

Existing network evolution models struggle to disentangle and quantify the dynamic, relative contributions of multiple co-occurring generative mechanisms in real-world temporal networks. Method: We propose an event-level hybrid mechanism inference framework that employs graph neural networks (GNNs) to enhance conditional density estimation, enabling Bayesian approximate inference of mechanism-specific weights for each edge formation event. The framework integrates domain knowledge while balancing interpretability and learnability. Contribution/Results: Our approach supports fine-grained, mechanism-aware modeling of network evolution. Experiments on multiple real-world temporal networks demonstrate its ability to accurately identify dominant mechanism combinations and their time-varying patterns, significantly outperforming baseline methods. It constitutes the first interpretable and generalizable tool for event-level mechanistic decomposition of network formation, advancing mechanistic analysis of complex network dynamics.

To address the challenges of modeling long-range dependencies and historical sensitivity in continuous-time dynamic networks, this paper proposes the first generative framework that embeds path-dependent marked Hawkes processes into the network evolution space. Methodologically, it employs a nonlinear, left-continuous conditional intensity function to jointly model structural and temporal evolution driven by self-exciting events, integrating continuous-time point process theory with numerical likelihood estimation techniques. Theoretically, we establish stability criteria for the proposed model; algorithmically, we design an efficient simulation procedure and a scalable parameter inference scheme. Experiments on conference social network data demonstrate that the model accurately captures the dynamic evolution of participant relationships, achieving statistically significant improvements over state-of-the-art baselines in both predictive accuracy and interpretability.

Real-world systems often exhibit complex interactions that transcend pairwise relationships, which conventional graph models struggle to capture effectively. This work presents a systematic review of graph-based modeling frameworks for higher-order networks, integrating diverse interaction paradigms—including simplicial, hierarchical, temporal, multilayer, recursive, and tensor-based representations—to clarify their structural principles and intrinsic connections. Building upon its first edition, this updated and comprehensive survey introduces key conceptual advances and refines theoretical formulations, thereby establishing a unified paradigm for higher-order network modeling. By offering a cohesive reference framework, the study significantly enhances the capacity to represent and analyze complex systems, supporting both theoretical development and practical applications in the field.

This work addresses the classical challenge of efficiently generating bipartite, directed, and undirected graphs that satisfy prescribed degree sequences when only local node-degree information is available. The authors propose a sequential graph construction method that, for the first time, rigorously characterizes the necessary and sufficient feasibility interval for the number of connections at each step, thereby guaranteeing global realizability while unifying the treatment of all three graph types. Building on this theoretical foundation, they develop a versatile algorithm capable of both exhaustive enumeration and uniform random sampling, supporting symmetric connections and scaling to large-scale instances. Experimental results demonstrate that the proposed approach substantially outperforms existing methods in computational efficiency and scalability, effectively overcoming the performance bottleneck in large-scale graph generation.

This work addresses the joint modeling of causal relationships and nonlinear dynamic dependencies among nodes, along with topology inference, in dynamic graph scenarios—such as brain networks, transportation systems, and financial markets—where the underlying graph structure is unknown. To overcome the limitations of conventional linear time-invariant models in capturing time-varying, nonlinear, and directed dependencies, we propose a unified framework based on kernel dictionary selection. The framework seamlessly integrates structural priors including sparsity, acyclicity, low-rankness, and graph smoothness, supporting both batch and online learning, and naturally extending to tensor representations. It unifies covariance selection, structural equation modeling, nonlinear vector autoregression, kernelized modeling, tensor decomposition, and convex optimization. Theoretically guaranteed convergence is established. Experiments demonstrate significant improvements in leveraging higher-order statistical information, enabling high-accuracy and interpretable inference of dynamic graph topologies.

This study addresses the limitation of traditional scale-free network models, which rely on node growth and preferential attachment and thus fail to capture real-world systems with fixed node counts but dynamically evolving links. To overcome this, the authors propose a dynamic network model based on state-dependent random walks, where node degree evolution is formulated as a stochastic process featuring stagnation and a variable diffusion coefficient. Theoretical analysis and numerical simulations demonstrate that, even on a fixed-size network, the model spontaneously generates a stable power-law degree distribution and successfully reproduces structural characteristics observed in three empirical networks. Furthermore, resilience assessments reveal that the model accurately captures network robustness under targeted attacks, thereby elucidating its intrinsic mechanisms of resilience.

This work addresses the challenge that existing link prediction models struggle to disentangle users’ intrinsic preferences from the amplification effect of algorithmic feedback on network homophily. The authors propose the first dynamic graph analysis framework based on a multivariate Hawkes process, which explicitly decouples users’ inherent interaction tendencies from algorithmic feedback mechanisms. Central to this approach is a novel bias metric driven by instantaneous interaction intensity, capturing real-time reinforcement dynamics beyond conventional cumulative measures. The framework is theoretically grounded, with formal proofs establishing the stability and convergence of the induced dynamics. Experimental results demonstrate that the proposed bias metric effectively quantifies the strength of algorithmic feedback under diverse link prediction strategies, offering a reliable tool for understanding how algorithms shape network evolution.

Existing approaches for critical node identification in dynamic and higher-order networks lack a unified methodological framework. Method: We systematically survey techniques across social, transportation, biological, and financial domains, and—based on methodological foundations and application contexts—categorize seven mainstream paradigms for the first time. We propose a unified analytical framework explicitly designed for dynamicity and higher-order structural dependencies. Contribution/Results: Our analysis identifies four core challenges: algorithmic generality, real-time evaluability, higher-order dependency modeling, and scalability to large-scale networks. Integrating centrality measures, influence maximization, network control theory, dynamic modeling, and AI-driven methods, we synthesize state-of-the-art advances and delineate three key future directions: time-aware modeling, lightweight and efficient algorithms, and interpretable machine learning integration.