The paper introduces a formal objective for detecting echo chambers in social networks, distinguishing it from community detection, graph cut, and clique problems. It employs Fourier transform theory of set functions to define the objective and proposes a scalable semidefinite relaxation solved with interior point methods and sparse linear algebra. Experiments on synthetic and real datasets show the algorithm outperforms existing methods in recovering ground‑truth echo chambers and producing better network properties, including higher agreement with suspended users.
arXiv:2602. 17104v2 Announce Type: replace-cross Abstract: We propose a streamlined spectral algorithm for community detection in the two-community stochastic block model (SBM) under constant edge density assumptions.
arXiv:2601. 03946v3 Announce Type: replace-cross Abstract: We consider the densest submatrix problem, which seeks the submatrix of fixed size of a given binary matrix that contains the most nonzero entries.
arXiv:2609.12445v1 Announce Type: cross Abstract: Community detection in bipartite networks is a fundamental problem in modern data analysis, with applications in recommendation systems, biological n...
The paper introduces the Echo Chamber Effect, a failure mode in Graph Neural Networks where intra-community representations collapse while inter-community separation remains, differing from traditional oversmoothing. It proposes the Echo Chamber Index (ECI) to detect this effect by stratifying pairwise distances by community membership. Building on this analysis, the authors present Community-Aware Split Propagation (CASP), a lightweight plugin that decouples intra- and inter-community aggregation and learns their balance from label structure, improving performance across various GNN backbones in both homophilic and heterophilic settings.
arXiv:2504. 19419v3 Announce Type: replace Abstract: Local clustering aims to identify specific substructures within a large graph without any additional structural information of the graph.
arXiv:2508. 02158v2 Announce Type: replace-cross Abstract: Detection of planted subgraphs in Erd\"os-R\'enyi random graphs has been extensively studied, leading to a rich body of results characterizing both statistical and computational thresholds.
arXiv:2609.23668v1 Announce Type: cross Abstract: Inferring network topology from noisy node observations is a central problem in graph signal processing. In this paper, we consider Laplacian-constra...
The paper presents provable guarantees for a spectral method that recovers binary node labels on signed graphs with edge‑flip noise. It provides graph‑structure‑agnostic bounds on approximate inference accuracy and maximum angle deviation, using matrix concentration and eigenvector perturbation techniques. The results connect to the Cheeger constant and are validated with synthetic experiments, marking the first theoretical analysis of this spectral approach.
The paper introduces a degree‑corrected joint matrix factorization technique for detecting communities in multilayer networks. It uses a nonnegative symmetric matrix trifactorization that enforces disjoint, shared communities across layers while allowing each layer to have distinct connectivity patterns and node degrees. An efficient algorithm is presented and evaluated on a multilayer degree‑corrected stochastic block model, showing superior performance compared to existing methods.
arXiv:2606. 27455v1 Announce Type: cross Abstract: We address the problem of inferring a directed network from nodal measurements generated by linear diffusion dynamics on the sought graph.
arXiv:2606. 01546v1 Announce Type: new Abstract: Sparse high-dimensional representations are conducive to uncovering nontrivial structures in unsupervised exploration of data.
arXiv:2607. 11938v1 Announce Type: cross Abstract: This book is about the mathematical foundations of data science.