Related papers: Finite graphs and amenability
In this note we elaborate on some notions of surface area for discrete graphs which are closely related to the inverse degree. These notions then naturally lead to associated connectivity measures of graphs and to the definition of a…
We analyze the universality and generalization of graph neural networks (GNNs) on attributed graphs, i.e., with node attributes. To this end, we propose pseudometrics over the space of all attributed graphs that describe the fine-grained…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
A novel approach to complex problems has been previously applied to graph classification and the graph equivalence problem. Here we consider its applications to a wide set of NP complete problems, namely, those of finding a subgraph g…
We initiate a quantitative study of measure equivalence (and orbit equivalence) between finitely generated groups, which extends the classical setting of $\mathrm L^p$ measure equivalence. In this paper, our main focus will be on amenable…
We provide an alternative proof for the extreme amenability of the unitary group of the hyperfinite II${}_1$-factor von Neumann algebra, endowed with the strong operator topology.
In the branch of mathematics known as graph theory, graphs are considered as a set of points, called vertices, with connections between these points, called edges. The purpose of this paper is to study mappings between two graphs that have…
Graph-theoretic tools and techniques have seen wide use in the multi-agent systems literature, and the unpredictable nature of some multi-agent communications has been successfully modeled using random communication graphs. Across both…
We prove that for any infinite, maximal amenable subgroup $H$ in a hyperbolic group $G$, the von Neumann subalgebra $LH$ is maximal amenable inside $LG$. It provides many new, explicit examples of maximal amenable subalgebras in II$_1$…
We outline some recent proofs of quantum ergodicity on large graphs and give new applications in the context of irregular graphs. We also discuss some remaining questions.
Pairwise comparison of graphs is key to many applications in Machine learning ranging from clustering, kernel-based classification/regression and more recently supervised graph prediction. Distances between graphs usually rely on…
This paper is a follow-up to our joint paper with I. Agol, P. Storm and K. Whyte "Finiteness of arithmetic hyperbolic reflection groups". The main purpose is to investigate the effective side of the method developed there and its possible…
A new approach to find all the transitive orientations for a comparability graph (finite or infinite) is presented. This approach is based on the link between the notion of ``strong'' partitive set and the forcing theory (notions of…
The operability of a network concerns its ability to remain operational, despite possible failures in its links or equipment. One may model the network through a graph to evaluate and increase this operability. Its vertices and edges…
The stability method is very useful for obtaining exact solutions of many extremal graph problems. Its key step is to establish the stability property which, roughly speaking, states that any two almost optimal graphs of the same order $n$…
We present a systematic study of the regularity phenomena for NIP hypergraphs and connections to the theory of (locally) generically stable measures, providing a model-theoretic hypergraph version of the results from [L. Lov\'asz, B.…
We present results concerning the expressiveness and decidability of a popular graph learning formalism, graph neural networks (GNNs), exploiting connections with logic. We use a family of recently-discovered decidable logics involving…
This paper presents a novel application of graph neural networks for modeling and estimating network heterogeneity. Network heterogeneity is characterized by variations in unit's decisions or outcomes that depend not only on its own…
Similarity search is a fundamental task for exploiting information in various applications dealing with graph data, such as citation networks or knowledge graphs. While this task has been intensively approached from heuristics to graph…
We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…