Related papers: Neutral Networks of Sequence to Shape Maps

Graph neural networks aim to learn representations for graph-structured data and show impressive performance, particularly in node classification. Recently, many methods have studied the representations of GNNs from the perspective of…

We establish a parametric framework for obtaining obstruction characterizations of graph parameters with respect to a quasi-ordering $\leqslant$ on graphs. At the center of this framework lies the concept of a $\leqslant$-parametric graph:…

A new heuristic based on vertex invariants is developed to rapidly distinguish non-isomorphic graphs to a desired level of accuracy. The method is applied to sample subgraphs from an E.coli protein interaction network, and as a probe for…

Graph Nerual Networks (GNNs) are effective models in graph embedding. It extracts shallow features and neighborhood information by aggregating neighbor information to learn the embedding representation of different nodes. However, the local…

This paper analyzes neural networks through graph variables and statistical sufficiency. We interpret neural network layers as graph-based transformations, where neurons act as pairwise functions between inputs and learned anchor points.…

Let $n$ be any positive integer, the friendship graph $F_n$ consist of $n$ edge-disjoint triangles that all of them meeting in one vertex. A graph $G$ is called cospectral with a graph $H$ if their adjacency matrices have the same…

This paper describes how realistic neuromorphic networks can have their connectivity properties fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the…

This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. Achieving such disentanglement leads to two unrelated advantages: i) a significant…

The Graph Minors Structure Theorem of Robertson and Seymour asserts that, for every graph $H,$ every $H$-minor-free graph can be obtained by clique-sums of ``almost embeddable'' graphs. Here a graph is ``almost embeddable'' if it can be…

We study the ratio, in a finite graph, of the sizes of the largest matching in any pair of disjoint matchings with the maximum total number of edges and the largest possible matching. Previously, it was shown that this ratio is between 4/5…

Real-world networks exhibit prominent hierarchical and modular structures, with various subgraphs as building blocks. Most existing studies simply consider distinct subgraphs as motifs and use only their numbers to characterize the…

We consider the routing of neutral atoms on a reconfigurable lattice in terms of hypergraph transformations. We prove the routing number of a Ramanujan $(d,r)$-regular hypergraph on $N$ vertices satisfies $\mathrm{rt}(H) = \Theta(\log N)$,…

We introduce an unsupervised graph embedding that trades off local node similarity and connectivity, and global structure. The embedding is based on a generalized graph Laplacian, whose eigenvectors compactly capture both network structure…

Recent studies show that Graph Neural Networks (GNNs) are vulnerable to adversarial attack, i.e., an imperceptible structure perturbation can fool GNNs to make wrong predictions. Some researches explore specific properties of clean graphs…

A map is a connected topological graph cellularly embedded in a surface and a complete map is a cellularly embedded complete graph in a surface. In this paper, all automorphisms of complete maps of order n are determined by permutations on…

The sorting number of a graph with $n$ vertices is the minimum depth of a sorting network with $n$ inputs and outputs that uses only the edges of the graph to perform comparisons. Many known results on sorting networks can be stated in…

Cycle consistency has long been exploited as a powerful prior for jointly optimizing maps within a collection of shapes. In this paper, we investigate its utility in the approaches of Deep Functional Maps, which are considered…

Spectral Graph Neural Networks (GNNs) are gaining attention for their ability to surpass the limitations of message-passing GNNs. They rely on supervision from downstream tasks to learn spectral filters that capture the graph signal's…

We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…

In this paper we study self-similar and fractal networks from the combinatorial perspective. We establish analogues of topological (Lebesgue) and fractal (Hausdorff) dimensions for graphs and demonstrate that they are naturally related to…