Community detection is an essential tool for unsupervised data exploration and revealing the organisational structure of networked systems. With a long history in network science, community detection typically relies on objective functions, optimised with custom-tailored search algorithms, but often without leveraging recent advances in deep learning. Recently, first works have started incorporating such objectives into loss functions for deep graph clustering and pooling. We consider the map equation, a popular information-theoretic objective function for unsupervised community detection, and express it in differentiable tensor form for optimisation through gradient descent. Our formulation turns the map equation compatible with any neural network architecture, enables end-to-end learning, incorporates node features, and chooses the optimal number of clusters automatically, all without requiring explicit regularisation. Applied to unsupervised graph clustering tasks, we achieve competitive performance against state-of-the-art deep graph clustering baselines in synthetic and real-world datasets.

While prior work on group recommender systems (GRSs) has primarily focused on improving recommendation accuracy, most approaches assume static or predefined groups, making them unsuitable for dynamic, real-world scenarios. We reframe group formation as a core challenge in GRSs and propose DeepForm (Stochastic Deep Graph Clustering for Practical Group Formation), a framework designed to meet three key operational requirements: (1) the incorporation of high-order user information, (2) real-time group formation, and (3) dynamic adjustment of the number of groups. DeepForm employs a lightweight GCN architecture that effectively captures high-order structural signals. Stochastic cluster learning enables adaptive group reconfiguration without retraining, while contrastive learning refines groups under dynamic conditions. Experiments on multiple datasets demonstrate that DeepForm achieves superior group formation quality, efficiency, and recommendation accuracy compared with various baselines.

Source code is publicly available as a module of ThinkMatch.

Community detection is an essential tool for unsupervised data exploration and revealing the organisational structure of networked systems. With a long history in network science, community detection typically relies on objective functions, optimised with custom-tailored search algorithms, but often without leveraging recent advances in deep learning. Recently, first works have started incorporating such objectives into loss functions for deep graph clustering and pooling. We consider the map equation, a popular information-theoretic objective function for unsupervised community detection, and express it in differentiable tensor form for optimisation through gradient descent. Our formulation turns the map equation compatible with any neural network architecture, enables end-to-end learning, incorporates node features, and chooses the optimal number of clusters automatically, all without requiring explicit regularisation.

Deep graph learning and network science both analyze graphs but approach similar problems from different perspectives. Whereas network science focuses on models and measures that reveal the organizational principles of complex systems with explicit assumptions, deep graph learning focuses on flexible and generalizable models that learn patterns in graph data in an automated fashion. Despite these differences, both fields share the same goal: to better model and understand patterns in graph-structured data. Early efforts to integrate methods, models, and measures from network science and deep graph learning indicate significant untapped potential. In this position, we explore opportunities at their intersection. We discuss open challenges in deep graph learning, including data augmentation, improved evaluation practices, higher-order models, and pooling methods. Likewise, we highlight challenges in network science, including scaling to massive graphs, integrating continuous gradient-based optimization, and developing standardized benchmarks.

Graph clustering is an essential aspect of network analysis that involves grouping nodes into separate clusters. Recent developments in deep learning have resulted in advanced deep graph clustering techniques, which have proven effective in many applications. Nonetheless, these methods often encounter difficulties when dealing with the complexities of real-world graphs, particularly in the presence of noisy edges. Additionally, many denoising graph clustering strategies tend to suffer from lower performance compared to their non-denoised counterparts, training instability, and challenges in scaling to large datasets. To tackle these issues, we introduce a new framework called the Dual Adaptive Assignment Approach for Robust Graph-Based Clustering (RDSA). RDSA consists of three key components: (i) a node embedding module that effectively integrates the graph's topological features and node attributes; (ii) a structure-based soft assignment module that improves graph modularity by utilizing an affinity matrix for node assignments; and (iii) a node-based soft assignment module that identifies community landmarks and refines node assignments to enhance the model's robustness. We assess RDSA on various real-world datasets, demonstrating its superior performance relative to existing state-of-the-art methods. Our findings indicate that RDSA provides robust clustering across different graph types, excelling in clustering effectiveness and robustness, including adaptability to noise, stability, and scalability.

Graph clustering, a classical task in graph learning, involves partitioning the nodes of a graph into distinct clusters. This task has applications in various real-world scenarios, such as anomaly detection, social network analysis, and community discovery. Current graph clustering methods commonly rely on module pre-training to obtain a reliable prior distribution for the model, which is then used as the optimization objective. However, these methods often overlook deeper supervised signals, leading to sub-optimal reliability of the prior distribution. To address this issue, we propose a novel deep graph clustering method called CGCN. Our approach introduces contrastive signals and deep structural information into the pre-training process. Specifically, CGCN utilizes a contrastive learning mechanism to foster information interoperability among multiple modules and allows the model to adaptively adjust the degree of information aggregation for different order structures. Our CGCN method has been experimentally validated on multiple real-world graph datasets, showcasing its ability to boost the dependability of prior clustering distributions acquired through pre-training. As a result, we observed notable enhancements in the performance of the model.

Dynamic community detection methods often lack effective mechanisms to ensure temporal consistency, hindering the analysis of network evolution. In this paper, we propose a novel deep graph clustering framework with temporal consistency regularization on inter-community structures, inspired by the concept of minimal network topological changes within short intervals. Specifically, to address the representation collapse problem, we first introduce MFC, a matrix factorization-based deep graph clustering algorithm that preserves node embedding. Based on static clustering results, we construct probabilistic community networks and compute their persistence homology, a robust topological measure, to assess structural similarity between them. Moreover, a novel neural network regularization TopoReg is introduced to ensure the preservation of topological similarity between inter-community structures over time intervals. Our approach enhances temporal consistency and clustering accuracy on real-world datasets with both fixed and varying numbers of communities. It is also a pioneer application of TDA in temporally persistent community detection, offering an insightful contribution to field of network analysis. Code and data are available at the public git repository: https://github.com/kundtx/MFC_TopoReg

Synthetic biologists and molecular programmers design novel nucleic acid reactions, with many potential applications. Good visualization tools are needed to help domain experts make sense of the complex outputs of folding pathway simulations of such reactions. Here we present ViDa, a new approach for visualizing DNA reaction folding trajectories over the energy landscape of secondary structures. We integrate a deep graph embedding model with common dimensionality reduction approaches, to map high-dimensional data onto 2D Euclidean space. We assess ViDa on two well-studied and contrasting DNA hybridization reactions. Our preliminary results suggest that ViDa's visualization successfully separates trajectories with different folding mechanisms, thereby providing useful insight to users, and is a big improvement over the current state-of-the-art in DNA kinetics visualization.