Related papers: The coupling method for inhomogeneous random inter…

In 1990 Bender, Canfield and McKay gave an asymptotic formula for the number of connected graphs on $[n]$ with $m$ edges, whenever $n$ and the nullity $m-n+1$ tend to infinity. Asymptotic formulae for the number of connected $r$-uniform…

A switching method is a graph operation that results in cospectral graphs (graphs with the same spectrum). Work by Wang and Xu [Discrete Math. 310 (2010)] suggests that most cospectral graphs with cospectral complements can be constructed…

Testing for independence between graphs is a problem that arises naturally in social network analysis and neuroscience. In this paper, we address independence testing for inhomogeneous Erd\H{o}s-R\'{e}nyi random graphs on the same vertex…

We propose a novel method for topological analysis of unweighted graphs which is based on \textit{persistent homology}. The proposed method maps the input graph to a complete weighted graph where the weighting function maps each edge to a…

We use the concept of a Kirchhoff resistor network (alternatively random walk on a network) to probe connected graphs and produce symmetry revealing canonical labelings of the graph(s) nodes and edges.

A new coupling rule for the Lighthill-Whitham-Richards model at merging junctions is introduced that imposes the preservation of the ratio between inflow from a given road to the total inflow into the junction. This rule is considered both…

We propose a random bipartite graph with weights assigned to both parts of the vertex sets. Edges are formed independently with probabilities that depend on these weights. This bipartite graph naturally gives rise to a random intersection…

This paper introduces a $K$-function for assessing second-order properties of inhomogeneous random measures generated by marked point processes. The marks can be geometric objects like fibers or sets of positive volume, and the presented…

We classify the countable ultrahomogeneous 2-vertex-colored graphs in which the color classes are imprimitive, i.e., up to complementation they form disjoint unions of cliques. This generalizes work by Jenkinson, Lockett and Truss as well…

This article discusses random hypergraphs with varying hyperedge sizes, admitting large hyperedges with size tending to infinity, and heavy-tailed limiting hyperedge size distributions. The main result describes a threshold for the random…

We study growth properties of the number of paths of lenght k for a variant of Cameo graphs introduced in an earlier paper. Sharp results are obtained for threshold for the k-path connectivity and the essential diameter.

We consider large random graphs with prescribed degrees, such as those generated by the configuration model. In the regime where the empirical degree distribution approaches a limit $\mu$ with finite mean, we establish the systematic…

We analyze the component evolution in inhomogeneous random intersection graphs when the average degree is close to 1. As the average degree increases, the size of the largest component in the random intersection graph goes through a phase…

This paper considers the problem of estimating multiple related Gaussian graphical models from a $p$-dimensional dataset consisting of different classes. Our work is based upon the formulation of this problem as group graphical lasso. This…

Random key graphs form a class of random intersection graphs and are naturally induced by the random key predistribution scheme of Eschenauer and Gligor for securing wireless sensor network (WSN) communications. Random key graphs have…

The $s$-point correlation function of a Gaussian Hermitian random matrix theory, with an external source tuned to generate a multi-critical singularity, provides the intersection numbers of the moduli space for the $p$-th spin curves…

We establish conditions on sequences of graphs which ensure that the mixing times of the random walks on the graphs in the sequence converge. The main assumption is that the graphs, associated measures and heat kernels converge in a…

This work derives an upper bound on the maximum cardinality of a family of graphs on a fixed number of vertices, in which the intersection of every two graphs in that family contains a subgraph that is isomorphic to a specified graph H.…

In 2009, two different groups independently explored the behavior of random threshold graphs. Here, we extend their techniques to find the distribution of other properties, including matching number, degeneracy, and length of the longest…

The random intersection graph model $\mathcal G(n,m,p)$ is considered. Due to substantial edge dependencies, studying even fundamental statistics such as the subgraph count is significantly more challenging than in the classical binomial…