Related papers: Graphons, cut norm and distance, couplings and rea…

We consider constrained variants of graph homomorphisms such as embeddings, monomorphisms, full homomorphisms, surjective homomorpshims, and locally constrained homomorphisms. We also introduce a new variation on this theme which derives…

We study four different notions of convergence for graphexes, recently introduced by Borgs, Chayes, Cohn and Holden, and by Veitch and Roy. We give some properties of them and some relations between them. We also extend results by Veitch…

We associate to a graphon $\gamma$ the sequence of $W$-random graphs $(G_n(\gamma))_{n \geq 1}$. We say that the graphon is singular if, for any finite graph $F$, the homomorphism density $t(F,G_n(\gamma))$ has a variance of order…

We consider the problem of estimating graph limits, known as graphons, from observations of sequences of sparse finite graphs. In this paper we show a simple method that can shed light on a subset of sparse graphs. The method involves…

There are several notions of convergence for sequences of bounded degree graphs. One such notion is left convergence, which is based on counting neighborhood distributions. Another notion is right convergence, based on counting…

Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph…

We prove measurable analogues of Whitney's classical theorems on weak isomorphisms of finite graphs. In the setting of locally finite graphings, we introduce a notion of weak isomorphism as an edge-measure-preserving Borel bijection that…

A general novel approach mapping discrete, combinatorial, graph-theoretic problems onto ``physical'' models - namely $n$ simplexes in $n-1$ dimensions - is applied to the graph equivalence problem. It is shown to solve this long standing…

The notions of bounded expansion and nowhere denseness not only offer robust and general definitions of uniform sparseness of graphs, they also describe the tractability boundary for several important algorithmic questions. In this paper we…

We present a new notion of limits of weighted directed graphs of growing size based on convergence of their random quotients. These limits are specified in terms of random exchangeable measures on the unit square. We call our limits…

We consider a generalization of the concept of $d$-flattenability of graphs - introduced for the $l_2$ norm by Belk and Connelly - to general $l_p$ norms, with integer $P$, $1 \le p < \infty$, though many of our results work for $l_\infty$…

We work out the graph limit theory for dense interval graphs. The theory developed departs from the usual description of a graph limit as a symmetric function $W(x,y)$ on the unit square, with $x$ and $y$ uniform on the interval $(0,1)$.…

As relational datasets modeled as graphs keep increasing in size and their data-acquisition is permeated by uncertainty, graph-based analysis techniques can become computationally and conceptually challenging. In particular, node centrality…

We investigate the relative computability of exchangeable binary relational data when presented in terms of the distribution of an invariant measure on graphs, or as a graphon in either $L^1$ or the cut distance. We establish basic…

We introduce a new variant of the coarse Baum-Connes conjecture designed to tackle coarsely disconnected metric spaces called the boundary coarse Baum-Connes conjecture. We prove this conjecture for many coarsely disconnected spaces that…

The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…

Finding structural similarities in graph data, like social networks, is a far-ranging task in data mining and knowledge discovery. A (conceptually) simple reduction would be to compute the automorphism group of a graph. However, this…

We consider the problem of classifying graphs using graph kernels. We define a new graph kernel, called the generalized shortest path kernel, based on the number and length of shortest paths between nodes. For our example classification…

Coverings of undirected graphs are used in distributed computing, and unfoldings of directed graphs in semantics of programs. We study these two notions from a graph theoretical point of view so as to highlight their similarities, as they…

We work out the theory of fractional isomorphism of graphons as a generalization to the classical theory of fractional isomorphism of finite graphs. The generalization is given in terms of homomorphism densities of finite trees and it is…