Related papers: A Model Theory Approach to Structural Limits
This paper describes a procedure that system developers can follow to translate typical mathematical representations of linearized control systems into logic theories. These theories are then used to verify system requirements and find…
Graph Neural Networks (GNNs) extend convolutional neural networks to operate on graphs. Despite their impressive performances in various graph learning tasks, the theoretical understanding of their generalization capability is still…
Deep learning's performance has been extensively recognized recently. Graph neural networks (GNNs) are designed to deal with graph-structural data that classical deep learning does not easily manage. Since most GNNs were created using…
In this paper, we deal with a notion of Banach space-valued mappings defined on a set consisting of finite graphs with uniformly bounded vertex degree. These functions will be endowed with certain boundedness and additivity criteria. We…
We introduce and study the concept which we call the splitting of a graph and compare algebraic properties of the edge ideals of graphs and those of their splitting graphs.
We propose a new approach for defining and searching clusters in graphs that represent real technological or transaction networks. In contrast to the standard way of finding dense parts of a graph, we concentrate on the structure of edges…
A graph is a mathematical object consisting of a set of vertices and a set of edges connecting vertices. Graphs can be drawn on paper in various ways, but until recently all published methods of drawing graphs have had undesirable…
We study hypergraph visualization via its topological simplification. We explore both vertex simplification and hyperedge simplification of hypergraphs using tools from topological data analysis. In particular, we transform a hypergraph to…
Experimental limits on supersymmetry and similar theories are difficult to set because of the enormous available parameter space and difficult to generalize because of the complexity of single points. Therefore, more phenomenological,…
We survey various aspects of infinite extremal graph theory and prove several new results. The lead role play the parameters connectivity and degree. This includes the end degree. Many open problems are suggested.
The aim of this paper is to develop a new axiomatization of planar geometry by reinterpreting the original axioms of Euclid. The basic concept is still that of a line segment but its equivalent notion of betweenness is viewed as a…
Various modularity matrices appeared in the recent literature on network analysis and algebraic graph theory. Their purpose is to allow writing as quadratic forms certain combinatorial functions appearing in the framework of graph…
Two classical concepts of centrality in a graph are the median and the center. The connected notions of the status and the radius of a graph seem to be in no relation. In this paper, however, we show a clear connection of both concepts, as…
The theory of graphons is an important tool in understanding properties of large networks. We investigate a power-law random graph model and cast it in the graphon framework. The distinctively different structures of the limit graph are…
We investigate the problem of drawing graphs in 2D and 3D such that their edges (or only their vertices) can be covered by few lines or planes. We insist on straight-line edges and crossing-free drawings. This problem has many connections…
Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…
Graphs, and sequences of growing graphs, can be used to specify the architecture of mathematical models in many fields including machine learning and computational science. Here we define structured graph "lineages" (ordered by level…
We use the theory of graph limits to study several quasi-random properties, mainly dealing with various versions of hereditary subgraph counts. The main idea is to transfer the properties of (sequences of) graphs to properties of graphons,…
We provide a comprehensive overview of current approaches and systems for combining graphs and time series data. We categorize existing systems into four architectural categories and analyze how these systems meet different requirements and…
Beyond-planarity focuses on the study of geometric and topological graphs that are in some sense nearly-planar. Here, planarity is relaxed by allowing edge crossings, but only with respect to some local forbidden crossing configurations.…