Related papers: Spectral Graph Complexity
Let $\mathcal{A}$ be a set of positive numbers. A graph $G$ is called an $\mathcal{A}$-embeddable graph in $\mathbb{R}^d$ if the vertices of $G$ can be positioned in $\mathbb{R}^d$ so that the distance between endpoints of any edge is an…
Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying…
Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent…
Hypergraphs, as a generalization of simplicial complexes, have long been a subject of interest in their geometric interpretation. The subdivision of simplicial complexes can, to some extent, provide insights into the geometry of simplicial…
The square of a connected graph $G$ is obtained from $G$ by adding an edge between every pair of vertices at distance $2$. In this paper we give some upper or lower bounds for the spectral radius of the square of connected graphs, trees and…
Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
We apply a Bethe-Peierls approach to statistical-mechanics models defined on random networks of arbitrary degree distribution and arbitrary correlations between the degrees of neighboring vertices. Using the NP-hard optimization problem of…
Research on graph representation learning has received a lot of attention in recent years since many data in real-world applications come in form of graphs. High-dimensional graph data are often in irregular form, which makes them more…
We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…
Graph neural networks have developed by leaps and bounds in recent years due to the restriction of traditional convolutional filters on non-Euclidean structured data. Spectral graph theory mainly studies fundamental graph properties using…
The transmission problem is a system of two second-order elliptic equations of two unknowns equipped with the Cauchy data on the boundary. After four decades of research motivated by scattering theory, the spectral properties of this…
Graph classification aims to categorise graphs based on their structure and node attributes. In this work, we propose to tackle this task using tools from graph signal processing by deriving spectral features, which we then use to design…
Using the spectral theory of weakly convergent sequences of finite graphs, we prove the uniform existence of the integrated density of states for a large class of infinite graphs.
The complexity of a graph is the number of its labeled spanning trees. In this work complexity is studied in settings that admit regular graphs. An exact formula is established linking complexity of the complement of a regular graph to…
We discuss the possibility of extending different versions of the Campbell-Magaard theorem, which have already been established in the context of semi-Riemannian geometry, to the context of Weyl's geometry. We show that some of the known…
Complex networks representing social interactions, brain activities, molecular structures have been studied widely to be able to understand and predict their characteristics as graphs. Models and algorithms for these networks are used in…
We define a (pseudo-)distance between graphs based on the spectrum of the normalized Laplacian, which is easy to compute or to estimate numerically. It can therefore serve as a rough classification of large empirical graphs into families…
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…
Graph embedding methods aim at finding useful graph representations by mapping nodes to a low-dimensional vector space. It is a task with important downstream applications, such as link prediction, graph reconstruction, data visualization,…