相关论文: Structure of large random hypergraphs

We provide a sufficient criterion for the unique parameter identification of combinatorially symmetric Hidden Markov Models based on the structure of their transition matrix. If the observed states of the chain form a zero forcing set of…

Many complex systems involve direct interactions among more than two entities and can be represented by hypergraphs, in which hyperedges encode higher-order interactions among an arbitrary number of nodes. To analyze structures and dynamics…

In this study, we investigate the problem of classifying, characterizing, and designing efficient algorithms for hard inference problems on planar graphs, in the limit of infinite size. The problem is considered hard if, for a deterministic…

We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be…

We propose the following model of a random graph on n vertices. Let F be a distribution in R_+^{n(n-1)/2} with a coordinate for every pair i$ with 1 \le i,j \le n. Then G_{F,p} is the distribution on graphs with n vertices obtained by…

We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its…

This paper provides an overview of results, concerning longest or heaviest paths, in the area of random directed graphs on the integers along with some extensions. We study first-order asymptotics of heaviest paths allowing weights both on…

Generative network models play an important role in algorithm development, scaling studies, network analysis, and realistic system benchmarks for graph data sets. The commonly used graph-based benchmark model R-MAT has some drawbacks…

For a $d$-uniform random hypergraph on $n$ vertices in which hyperedges are included i.i.d.\ so that the average degree in the hypergraph is $n^{\delta+o(1)}$, the projection of such a hypergraph is a graph on the same $n$ vertices where an…

We study the asymptotics of large, moderate and normal deviations for the connected components of the sparse random graph by the method of stochastic processes. We obtain the logarithmic asymptotics of large deviations of the joint…

For $n\geq 3$, let $r=r(n)\geq 3$ be an integer. A hypergraph is $r$-uniform if each edge is a set of $r$ vertices, and is said to be linear if two edges intersect in at most one vertex. In this paper, the number of linear $r$-uniform…

Graphs are a standard framework for describing dynamical processes shaped by pairwise interactions among agents. But many systems involve interactions in groups of three or more agents. Here, we develop a method of "$\ell$-hyperedge…

Consider an N-dimensional Markov chain obtained from N one-dimensional random walks by Doob h-transform with the q-Vandermonde determinant. We prove that as N becomes large, these Markov chains converge to an infinite-dimensional Feller…

We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size…

Here we introduce simple structures for the analysis of complex hypergraphs, hypergraph animals. These structures are designed to describe the local node neighbourhoods of nodes in hypergraphs. We establish their relationships to lattice…

Mechanistic interpretability seeks to reverse-engineer neural network computations into human-understandable algorithms, yet extracting sparse computational circuits from billion-parameter language models remains challenging due to…

We consider a natural model of inhomogeneous random graphs that extends the classical Erd\H os-R\'enyi graphs and shares a close connection with the multiplicative coalescence, as pointed out by Aldous [AOP 1997]. In this model, the…

We introduce the notion of Levenshtein graphs, an analog to Hamming graphs but using the edit distance instead of the Hamming distance; in particular, Levenshtein graphs allow for underlying strings (nodes) of different lengths. We…

For real application and theoretical investigation of ordinary hypergraphs and non-ordinary hypergraphs, researchers need to establish standard rules and feasible operating methods. We propose a visualization tool for investigating…

Most causal discovery procedures assume that there are no latent confounders in the system, which is often violated in real-world problems. In this paper, we consider a challenging scenario for causal structure identification, where some…