Related papers: A class of models for random hypergraphs
This paper discusses the reliability of a graph in which the links are perfectly reliable but the nodes may fail with certain probability p. Calculating graph node reliability is an NP-Hard problem. We introduce an efficient and accurate…
The dissertation is related to combinatorial geometry with a strong probabilistic flavor. The main results can be split into three parts. The results of the first part guarantee that each "unit distance graph" in the plane has an induced…
Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of…
We study the level spacing distribution p(s) in the spectrum of random networks. According to our numerical results, the shape of p(s) in the Erdos-Renyi (E-R) random graph is determined by the average degree <k>, and p(s) undergoes a…
We describe a new family of $k$-uniform hypergraphs with independent random edges. The hypergraphs have a high probability of being peelable, i.e. to admit no sub-hypergraph of minimum degree $2$, even when the edge density (number of edges…
In complex social systems encoded as hypergraphs, higher-order (i.e., group) interactions taking place among more than two individuals are represented by hyperedges. One of the higher-order correlation structures native to hypergraphs is…
In this paper we study the component structure of random graphs with independence between the edges. Under mild assumptions, we determine whether there is a giant component, and find its asymptotic size when it exists. We assume that the…
Random graphs with a given degree sequence are often constructed using the configuration model, which yields a random multigraph. We may adjust this multigraph by a sequence of switchings, eventually yielding a simple graph. We show that,…
Mean-field frozen percolation is a random graph-valued process, which adjusts the dynamics of the classical Erdos-Renyi process with an additional mechanism to 'freeze' potential giant components before they can form. It is known to exhibit…
The presence of unobserved node specific heterogeneity in Exponential Random Graph Models (ERGM) is a general concern, both with respect to model validity as well as estimation instability. We therefore extend the ERGM by including node…
In many real world datasets arising from social networks, there are hidden higher order relations among data points which cannot be captured using graph modeling. It is natural to use a more general notion of hypergraphs to model such…
The random graph of Erdos and Renyi is one of the oldest and best studied models of a network, and possesses the considerable advantage of being exactly solvable for many of its average properties. However, as a model of real-world networks…
Hypergraphs tackle the limitations of traditional graphs by introducing {\em hyperedges}. While graph edges connect only two nodes, hyperedges connect an arbitrary number of nodes along their edges. Also, the underlying message-passing…
Comparative analysis between a network and a random graph model can uncover network properties that significantly deviate from those in random networks. The standard random graph model used for comparison uniformly samples random graphs…
This work will appear as a chapter in a forthcoming volume titled "Topics in Probabilistic Graph Theory". A theory of scaling limits for random graphs has been developed in recent years. This theory gives access to the large-scale geometric…
Despite the prevalence of hypergraphs in a variety of high-impact applications, there are relatively few works on hypergraph representation learning, most of which primarily focus on hyperlink prediction, often restricted to the…
In this paper, we develop a novel paradigm, namely hypergraph shift, to find robust graph modes by probabilistic voting strategy, which are semantically sound besides the self-cohesiveness requirement in forming graph modes. Unlike the…
The problem of continuum percolation in dispersions of rods is reformulated in terms of weighted random geometric graphs. Nodes (or sites or vertices) in the graph represent spatial locations occupied by the centers of the rods. The…
In this note we define and study graph invariants generalizing to higher dimension the maximum degree of a vertex and the vertex-connectivity (our $0$-dimensional cases). These are known to coincide almost surely in any regime for…
We introduce a class of random graphs that we argue meets many of the desiderata one would demand of a model to serve as the foundation for a statistical analysis of real-world networks. The class of random graphs is defined by a…