Related papers: Maximal Pivots on Graphs with an Application to Ge…
In this paper, we introduce a magneto-spectral invariant for finite graphs. This invariant vanishes on trees and is maximized by complete graphs. We compute this invariant for cycles, complete graphs, wheel graphs, hypercubes, complete…
We study the challenges of applying deep learning to gene expression data. We find experimentally that there exists non-linear signal in the data, however is it not discovered automatically given the noise and low numbers of samples used in…
We explicitly construct parameter transformations between gradient flows in metric spaces, called curves of maximal slope, having different exponents when the associated function satisfies a suitable convexity condition. These…
We give an explicit calculation of the Wu invariants for immersions of a finite graph into the plane and classify all generic immersions of a graph into the plane up to regular homotopy by the Wu invariant. This result is a generalization…
We introduce a novel class of rotation invariants of two dimensional curves based on iterated integrals. The invariants we present are in some sense complete and we describe an algorithm to calculate them, giving explicit computations up to…
The operation of transforming one spanning tree into another by replacing an edge has been considered widely, both for general and planar straight-line graphs. For the latter, several variants have been studied (e.g., edge slides and edge…
Random graphs with a given degree sequence are often constructed using the configuration model, which yields a random multigraph. We may adjust this multigraph by a sequence of switchings, eventually yielding a simple graph. We show that,…
Graph processing is used extensively in areas from social networking mining to web indexing. We demonstrate that the performance and dependability of such applications critically hinges on the graph data structure used, because a fixed,…
We study the percolation properties of graph partitioning on random regular graphs with N vertices of degree $k$. Optimal graph partitioning is directly related to optimal attack and immunization of complex networks. We find that for any…
We provide a novel approach to construct generative models for graphs. Instead of using the traditional probabilistic models or deep generative models, we propose to instead find an algorithm that generates the data. We achieve this using…
These notes concern aspects of various graphs whose vertex set is a group $G$ and whose edges reflect group structure in some way (so that they are invariant under the action of the automorphism group of $G$). The graphs I will discuss are…
Traditional representations of graphs and their duals suggest the requirement that the dual vertices be placed inside their corresponding primal faces, and the edges of the dual graph cross only their corresponding primal edges. We consider…
Motion planning is a fundamental problem of robotics with applications in many areas of computer science and beyond. Its restriction to graphs has been investigated in the literature for it allows to concentrate on the combinatorial problem…
Version Control Systems, such as Git and Mercurial, manage the history of a project as a Directed Acyclic Graph encoding the various divergences and synchronizations happening in its life cycle. A popular workflow in the industry, called…
A graph is said to be nearly complete bipartite if it can be obtained by deleting a set of independent edges from a complete bipartite graph. The nonorientable genus of such graphs is known except in a few cases where the sizes of the…
We show that viewing graphs as sets of node features and incorporating structural and positional information into a transformer architecture is able to outperform representations learned with classical graph neural networks (GNNs). Our…
We classify row-finite Leavitt path algebras associated to graphs with no more than two vertices. For the discussion we use the following invariants: decomposability, the $K_0$ group, $\det(N'_E)$ (included in the Franks invariants), the…
This paper investigates the feasibility of using Graph Neural Networks (GNNs) for classical motion planning problems. We propose guiding both continuous and discrete planning algorithms using GNNs' ability to robustly encode the topology of…
Mixed graphs can be seen as digraphs with arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are bipartite and in which the undirected and directed degrees are one. The best graphs,…
We tackle the problem of simultaneous transformations of networks represented as graphs. Roughly speaking, one may distinguish two kinds of simultaneous or parallel rewrite relations over complex structures such as graphs: (i) those which…