Related papers: Eigencone Constellations on Ranked Spheres
The spectral properties of signed directed graphs, which may be naturally obtained by assigning a sign to each edge of a directed graph, have received substantially less attention than those of their undirected and/or unsigned counterparts.…
We define and study exact, efficient representations of realization spaces Euclidean Distance Constraint Systems (EDCS), which includes Linkages and Frameworks. Each representation corresponds to a choice of Cayley parameters and yields a…
To construct dispersion relations for diffusion or oscillation processes on random networks, it is necessary to obtain effective length scales for the eigenvectors of a graph Laplacian matrix, whose eigenvalues represent inverse time…
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…
State-of-the-art coronagraphs employed on extreme adaptive optics enabled instruments, are constantly improving the contrast detection limit for companions at ever closer separations to the host star. In order to constrain their properties…
Community Detection algorithms are used to detect densely connected components in complex networks and reveal underlying relationships among components. As a special type of networks, spatial networks are usually generated by the…
We introduce hierarchical neighbor graphs, a new architecture for connecting ad hoc wireless nodes distributed in a plane. The structure has the flavor of hierarchical clustering and requires only local knowledge and minimal computation at…
The classification of electron systems according to their topology has been at the forefront of condensed matter research in recent years. It has been found that systems of the same symmetry, previously thought of as equivalent, may in fact…
An embedding is a mapping from a set of nodes of a network into a real vector space. Embeddings can have various aims like capturing the underlying graph topology and structure, node-to-node relationship, or other relevant information about…
The study of random landscapes has long relied on counting stationary points: metastable states and the barriers between them. However, this method is useless for describing flat regions, common in constraint satisfaction problems. We…
Starting from a finite simple graph $G$, for each eigenvalue $\theta$ of its adjacency matrix one can construct a convex polytope $P_G(\theta)$, the so called $\theta$-eigenpolytop of $G$. For some polytopes this technique can be used to…
This article gives the construction and complete classification of all three-dimensional spherical manifolds, and orders them by decreasing volume, in the context of multiconnected universe models with positive spatial curvature. It…
Direct detection of exoplanets requires high dynamic range imaging. Coronagraphs could be the solution, but their performance in space is limited by wavefront errors (manufacturing errors on optics, temperature variations, etc.), which…
We introduce several novel and computationally efficient methods for detecting "core--periphery structure" in networks. Core--periphery structure is a type of mesoscale structure that includes densely-connected core vertices and…
Spectral analysis of networks states that many structural properties of graphs, such as centrality of their nodes, are given in terms of their adjacency matrices. The natural extension of such spectral analysis to higher order networks is…
A set of points $S$ in $d$-dimensional Euclidean space $\mathbb{R}^d$ is called a 2-distance set if the set of pairwise distances between the points has cardinality two. The 2-distance set is called spherical if its points lie on the unit…
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…
The monography examines the problem of constructing a group of automorphisms of a graph. A graph automorphism is a mapping of a set of vertices onto itself that preserves adjacency. The set of such automorphisms forms a vertex group of a…
Graph classification is a fundamental but challenging issue for numerous real-world applications. Despite recent great progress in image/video classification, convolutional neural networks (CNNs) cannot yet cater to graphs well because of…
Partitioning a graph into groups of vertices such that those within each group are more densely connected than vertices assigned to different groups, known as graph clustering, is often used to gain insight into the organisation of large…