Related papers: Optimal couplings between sparse block models
We investigate random connected graphs from a block-stable class whose distribution is weighted based on the number of $2$-connected components, or blocks. This includes the class of planar graphs. For this, we develop a notion of a…
The configuration model is the most natural model to generate a random multigraph with a given degree sequence. We use the notion of dense graph limits to characterize the special form of limit objects of convergent sequences of…
Exponential random graphs are important to model the structure of real-world complex networks. Here we solve the two-star model with degree-degree correlations in the sparse regime. The model constraints the average correlation between the…
We consider community detection from multiple correlated graphs sharing the same community structure. The correlated graphs are generated by independent subsampling of a parent graph sampled from the stochastic block model. The vertex…
Bootstrap percolation provides an emblematic instance of phase behavior characterised by an abrupt transition with diverging critical fluctuations. This unusual hybrid situation generally occurs in particle systems in which the occupation…
We consider the problem of community detection in the Stochastic Block Model with a finite number $K$ of communities of sizes linearly growing with the network size $n$. This model consists in a random graph such that each pair of vertices…
Random graph models are used to describe the complex structure of real-world networks in diverse fields of knowledge. Studying their behavior and fitting properties are still critical challenges, that in general, require model specific…
We consider randomized dynamics over the $n$-simplex, where at each step a random set, or block, of coordinates is evenly averaged. When all blocks have size 2, this reduces to the repeated averages studied in [CDSZ22], a version of the…
We consider the task of learning latent community structure from multiple correlated networks. First, we study the problem of learning the latent vertex correspondence between two edge-correlated stochastic block models, focusing on the…
For random graphs distributed according to a stochastic block model, we consider the inferential task of partioning vertices into blocks using spectral techniques. Spectral partioning using the normalized Laplacian and the adjacency matrix…
With the advent of structured data in the form of social networks, genetic circuits and protein interaction networks, statistical analysis of networks has gained popularity over recent years. Stochastic block model constitutes a classical…
We study the graph alignment problem over two independent Erd\H{o}s-R\'enyi graphs on $n$ vertices, with edge density $p$ falling into two regimes separated by the critical window around $p_c=\sqrt{\log n/n}$. Our result reveals an…
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…
We discuss the problem of embedding graphs in the plane with restrictions on the vertex mapping. In particular, we introduce a technique for drawing planar graphs with a fixed vertex mapping that bounds the number of times edges bend. An…
The labeled stochastic block model is a random graph model representing networks with community structure and interactions of multiple types. In its simplest form, it consists of two communities of approximately equal size, and the edges…
We consider the spectral properties of balanced stochastic block models of which the average degree grows slower than the number of nodes (sparse regime) or proportional to it (dense regime). For both regimes, we prove a phase transition of…
We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…
In this paper, we study convergence of coupled dynamical systems on convergent sequences of graphs to a continuum limit. We show that the solutions of the initial value problem for the dynamical system on a convergent graph sequence tend to…
This article establishes the performance of stochastic blockmodels in addressing the co-clustering problem of partitioning a binary array into subsets, assuming only that the data are generated by a nonparametric process satisfying the…
We extend the latent position random graph model to the line graph of a random graph, which is formed by creating a vertex for each edge in the original random graph, and connecting each pair of edges incident to a common vertex in the…