Related papers: Local Hyper-Flow Diffusion
While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect…
In this work we study statistical properties of graph-based clustering algorithms that rely on the optimization of balanced graph cuts, the main example being the optimization of Cheeger cuts. We consider proximity graphs built from data…
In this paper, we study the local linear convergence properties of a versatile class of Primal-Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of…
Influence maximization (IM) is a fundamental problem in complex network analysis, with a wide range of real-world applications. To date, existing approaches to influential node identification in IM have predominantly relied on standard…
Denoising-based models, including diffusion and flow matching, have led to substantial advances in graph generation. Despite this progress, such models remain constrained by two fundamental limitations: a computational cost that scales…
This paper is devoted to expressiveness of hypergraphs for which uncertainty propagation by local computations via Shenoy/Shafer method applies. It is demonstrated that for this propagation method for a given joint belief distribution no…
The hypergraph community detection problem seeks to identify groups of related nodes in hypergraph data. We propose an information-theoretic hypergraph community detection algorithm which compresses the observed data in terms of community…
Hypergraphs are a common model for multiway relationships in data, and hypergraph semi-supervised learning is the problem of assigning labels to all nodes in a hypergraph, given labels on just a few nodes. Diffusions and label spreading are…
The linear preferential attachment hypothesis has been shown to be quite successful to explain the existence of networks with power-law degree distributions. It is then quite important to determine if this mechanism is the consequence of a…
In this paper, we consider sparse networks consisting of a finite number of non-overlapping communities, i.e. disjoint clusters, so that there is higher density within clusters than across clusters. Both the intra- and inter-cluster edge…
Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods…
We study the statistical and computational properties of a network Lasso method for local graph clustering. The clusters delivered by nLasso can be characterized elegantly via network flows between cluster boundary and seed nodes. While…
For many random graph models, the analysis of a related birth process suggests local sampling algorithms for the size of, e.g., the giant connected component, the $k$-core, the size and probability of an epidemic outbreak, etc. In this…
Hypergraphs play a pivotal role in the modelling of data featuring higher-order relations involving more than two entities. Hypergraph neural networks emerge as a powerful tool for processing hypergraph-structured data, delivering…
Many networks can be characterised by the presence of communities, which are groups of units that are closely linked. Identifying these communities can be crucial for understanding the system's overall function. Recently, hypergraphs have…
Hypergraphs naturally arise when studying group relations and have been widely used in the field of machine learning. To the best of our knowledge, the recently proposed edge-dependent vertex weights (EDVW) modeling is one of the most…
In this paper, we propose a local model reduction approach for subsurface flow problems in stochastic and highly heterogeneous media. To guarantee the mass conservation, we consider the mixed formulation of the flow problem and aim to solve…
How can we accurately estimate local triangles for all nodes in simple and multigraph streams? Local triangle counting in a graph stream is one of the most fundamental tasks in graph mining with important applications including anomaly…
Graphs have become increasingly popular in modeling structures and interactions in a wide variety of problems during the last decade. Graph-based clustering and semi-supervised classification techniques have shown impressive performance.…
This paper establishes the consistency of a family of graph-cut-based algorithms for clustering of data clouds. We consider point clouds obtained as samples of a ground-truth measure. We investigate approaches to clustering based on…