Related papers: Combinatorial identities using Bernoulli Graphs

We study the problem of recovering the relative positions of objects moving along the real line based only on pairwise collision data. While interaction-based sensing systems arise naturally in a variety of practical settings, a systematic…

A complex unit gain graph is a simple graph in which each orientation of an edge is given a complex number with modulus 1 and its inverse is assigned to the opposite orientation of the edge. In this article, first we establish bounds for…

This paper introduces a new graph construction, the permutational power of a graph, whose adjacency matrix is obtained by the composition of a permutation matrix with the adjacency matrix of the graph. It is shown that this construction…

Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with…

Graphs from complex systems often share a partial underlying structure across domains while retaining individual features. Thus, identifying common structures can shed light on the underlying signal, for instance, when applied to scientific…

We consider complete graphs with edge weights and/or node weights taking values in some set. In the first part of this paper, we show that a large number of graphs are completely determined, up to isomorphism, by the distribution of their…

We study the structure of the asymptotic expansion of the probability that a combinatorial object is connected. We show that the coefficients appearing in those asymptotics are integers and can be interpreted as the counting sequences of…

In this work, we present a probabilistic model for directed graphs where nodes have attributes and labels. This model serves as a generative classifier capable of predicting the labels of unseen nodes using either maximum likelihood or…

We present a simple combinatorial model for quasipositive surfaces and positive braids, based on embedded bipartite graphs. As a first application, we extend the well-known duality on standard diagrams of torus links to twisted torus links.…

We introduce and investigate generalizations of interval and proper interval graphs to simplicial complexes, including strong interval, unit interval, and under closed variants. Through equivalent combinatorial and algebraic…

Ideas of Kn\"odel and B\"ohm-Hornik about walks in certain graphs, resembling the classical symmetric random walk on the integers, are combined. All the relevant generating functions (although occasionally quite involved) are made fully…

We give a simple statistical proof of a binomial identity, by evaluating the Laplace transform of the maximum of n independent exponential random variables in two different ways. As a by product, we obtain a simple proof of an interesting…

Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet…

Graphs provide an efficient tool for object representation in various computer vision applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a…

We give an overview of combinatorial methods to represent 3D data, such as graphs and meshes, from the viewpoint of their amenability to analysis using machine learning algorithms. We highlight pros and cons of various representations and…

Paper proposes a model of large networks based on a random preferential attachment graph with addition of complete subgraphs (cliques). The proposed model refers to models of random graphs following the nonlinear preferential attachment…

Binary data are highly common in many applications, however it is usually modelled with the assumption that the data are independently and identically distributed. This is typically not the case in many real-world examples and such the…

Dynamic graphs provide a flexible data abstraction for modelling many sorts of real-world systems, such as transport, trade, and social networks. Graph neural networks (GNNs) are powerful tools allowing for different kinds of prediction and…

In this paper, we derive eight basic identities of symmetry in three variables related to Bernoulli polynomials and power sums. These and most of their corollaries are new, since there have been results only about identities of symmetry in…

Inferring graph structure from observations on the nodes is an important and popular network science task. Departing from the more common inference of a single graph and motivated by social and biological networks, we study the problem of…