相关论文: Sparse random hypergraphs: Non-backtracking spectr…

In this paper, we study community detection when we observe $m$ sparse networks and a high dimensional covariate matrix, all encoding the same community structure among $n$ subjects. In the asymptotic regime where the number of features $p$…

We consider the problem of identifying underlying community-like structures in graphs. Towards this end we study the Stochastic Block Model (SBM) on $k$-clusters: a random model on $n=km$ vertices, partitioned in $k$ equal sized clusters,…

Consider a network where the nodes split into $K$ different communities. The community labels for the nodes are unknown and it is of major interest to estimate them (i.e., community detection). Degree Corrected Block Model (DCBM) is a…

Complex networks often exhibit community structure, with communities corresponding to denser subgraphs in which nodes are closely linked. When modelling systems where interactions extend beyond node pairs to arbitrary numbers of nodes,…

A sparse stochastic block model (SBM) with two communities is defined by the community probability $\pi_0,\pi_1$, and the connection probability between communities $a,b\in\{0,1\}$, namely $q_{ab} = \frac{\alpha_{ab}}{n}$. When $q_{ab}$ is…

We prove an analogue of Alon's spectral gap conjecture for random bipartite, biregular graphs. We use the Ihara-Bass formula to connect the non-backtracking spectrum to that of the adjacency matrix, employing the moment method to show there…

We provide a rearrangement based algorithm for fast detection of subgraphs of $k$ vertices with long escape times for directed or undirected networks. Complementing other notions of densest subgraphs and graph cuts, our method is based on…

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…

Community detection is crucial in data mining. Traditional methods primarily focus on graph structure, often neglecting the significance of attribute features. In contrast, deep learning-based approaches incorporate attribute features and…

Spectral clustering is a standard approach to label nodes on a graph by studying the (largest or lowest) eigenvalues of a symmetric real matrix such as e.g. the adjacency or the Laplacian. Recently, it has been argued that using instead a…

With the emergence of social networks, online platforms dedicated to different use cases, and sensor networks, the emergence of large-scale graph community detection has become a steady field of research with real-world applications.…

We study the hierarchy of communities in real-world networks under a generic stochastic block model, in which the connection probabilities are structured in a binary tree. Under such model, a standard recursive bi-partitioning algorithm is…

Community detection is a fundamental task in data analysis, and block models provide an approach for identifying a wide variety of community structures while offering high interpretability. The degree-corrected block model (DCBM) is an…

Community detection in graphs has many important and fundamental applications including in distributed systems, compression, image segmentation, divide-and-conquer graph algorithms such as nested dissection, document and word clustering,…

The community detection problem requires to cluster the nodes of a network into a small number of well-connected "communities". There has been substantial recent progress in characterizing the fundamental statistical limits of community…

The problem of community detection receives great attention in recent years. Many methods have been proposed to discover communities in networks. In this paper, we propose a Gaussian stochastic blockmodel that uses Gaussian distributions to…

A relevant, sometimes overlooked, quality criterion for communities in graphs is that they should be well-connected in addition to being edge-dense. Prior work has shown that leading community detection methods can produce poorly-connected…

We consider graphs with two communities and analyze an algorithm for learning the community labels when the edges of the graph and only a small fraction of the labels are known in advance. The algorithm is based on the Glauber dynamics for…

The stochastic block model is a natural model for studying community detection in random networks. Its clustering properties have been extensively studied in the statistics, physics and computer science literature. Recently this area has…

We consider three distinct and well studied problems concerning network structure: community detection by modularity maximization, community detection by statistical inference, and normalized-cut graph partitioning. Each of these problems…