Related papers: Sparse random graphs with clustering

Limiting distributions are derived for the sparse connected components that are present when a random graph on $n$ vertices has approximately $\half n$ edges. In particular, we show that such a graph consists entirely of trees, unicyclic…

Discovering the underlying structures present in large real world graphs is a fundamental scientific problem. In this paper we show that a graph's clique tree can be used to extract a hyperedge replacement grammar. If we store an ordering…

We propose algorithms for construction and random generation of hypergraphs without loops and with prescribed degree and dimension sequences. The objective is to provide a starting point for as well as an alternative to Markov chain Monte…

How can we approximate sparse graphs and sequences of sparse graphs (with unbounded average degree)? We consider convergence in the first $k$ moments of the graph spectrum (equivalent to the numbers of closed $k$-walks) appropriately…

We consider the random hypergraph on a finite vertex set by choosing each set of vertices as an hyperedge independently at random. We express the probability distributions of the (lower-)associated simplicial complex and the…

We study the random graph obtained by random deletion of vertices or edges from a random graph with given vertex degrees. A simple trick of exploding vertices instead of deleting them, enables us to derive results from known results for…

Inhomogeneous random graphs are fundamental models for real-world networks, where prescribed degrees are imposed as soft constraints. A common assumption in such models is that the degree distribution follows a power-law, capturing the…

This paper concerns the large deviations of a system of interacting particles on a random graph. There is no stochasticity, and the only sources of disorder are the random graph connections, and the initial condition. The average number of…

Many popular network models rely on the assumption of (vertex) exchangeability, in which the distribution of the graph is invariant to relabelings of the vertices. However, the Aldous-Hoover theorem guarantees that these graphs are dense or…

In this paper we consider a simple model of random graph process with {\it hard} copying as follows: At each time step $t$, with probability $0<\alpha\leq 1$ a new vertex $v_t$ is added and $m$ edges incident with $v_t$ are added in the…

We propose a wide class of preferential attachment models of random graphs, generalizing previous approaches. Graphs described by these models obey the power-law degree distribution, with the exponent that can be controlled in the models.…

In this paper, we study the edge eigenvalues of random geometric graphs (RGGs) generated by multivariate Gaussian samples in the sparse regime under a broad class of distance metrics. Previous work on edge eigenvalues under related setups…

Models for generating simple graphs are important in the study of real-world complex networks. A well established example of such a model is the erased configuration model, where each node receives a number of half-edges that are connected…

Traditional random graph models of networks generate networks that are locally tree-like, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly…

In this work, we introduce a novel evaluation framework for generative models of graphs, emphasizing the importance of model-generated graph overlap (Chanpuriya et al., 2021) to ensure both accuracy and edge-diversity. We delineate a…

Real social networks are often compared to random graphs in order to assess whether their typological structure could be the result of random processes. However, an Erd\H{o}s-R\'enyi random graph in large scale is often lack of local…

In this paper, we study a bipartite analogue of the `random graphs evolving by degrees' process. We are given a bipartitioned set of vertices $V$ into two disjoint parts ${L}$ and ${R}$ and possibly unequal positive constants $\alpha$ and…

Real-world networks, like social networks or the internet infrastructure, have structural properties such as large clustering coefficients that can best be described in terms of an underlying geometry. This is why the focus of the…

We study the problem of generating connected random graphs with no self-loops or multiple edges and that, in addition, have a given degree sequence. The generation method we focus on is the edge-switching Markov-chain method, whose…

In this paper we focus on the problem of finding (small) subhypergraphs in a (large) hypergraph. We use this problem to illustrate that reducing hypergraph problems to graph problems by working with the 2-section is not always a reasonable…