Related papers: Ramanujan Graphs and the Spectral Gap of Supercomp…
The inverse eigenvalue problem of a graph studies the real symmetric matrices whose off-diagonal pattern is prescribed by the adjacencies of the graph. The strong spectral property (SSP) is an important tool for this problem. This note…
Beyond-planarity focuses on combinatorial properties of classes of non-planar graphs that allow for representations satisfying certain local geometric or topological constraints on their edge crossings. Beside the study of a specific graph…
In this brief paper we present some results on creating and manipulating spectral gaps for a (regular) quantum graph by inserting appropriate internal structures into its vertices. Complete proofs and extensions of the results are planned…
For a graph $G$, its spectral radius $\rho(G)$ is the largest eigenvalue of its adjacency matrix. Let $\mathcal{F}$ be a finite family of graphs with $\min_{F\in \mathcal{F}}\chi(F)=r+1\geq3$, where $\chi(F)$ is the chromatic number of $F$.…
Some recent results on graph eigenvalues are improved. In particular, among all graphs of given order with no cliques of order $(r+1)$ the $r$-partite Turan graph has maximal spectral radius.
As graphical summaries for topological spaces and maps, Reeb graphs are common objects in the computer graphics or topological data analysis literature. Defining good metrics between these objects has become an important question for…
Graphs are a representation of structured data that captures the relationships between sets of objects. With the ubiquity of available network data, there is increasing industrial and academic need to quickly analyze graphs with billions of…
Hypergraphs require higher-dimensional representations, which makes it more difficult to compute and interpret their spectral properties. This survey article uses the framework of hypermatrices to give an in-depth overview of the spectral…
The \emph{thinness} of a graph is a width parameter that generalizes some properties of interval graphs, which are exactly the graphs of thinness one. Graphs with thinness at most two include, for example, bipartite convex graphs. Many…
A key feature of neural network architectures is their ability to support the simultaneous interaction among large numbers of units in the learning and processing of representations. However, how the richness of such interactions trades off…
The spectral theory of graphs provides a bridge between classical signal processing and the nascent field of graph signal processing. In this paper, a spectral graph analogy to Heisenberg's celebrated uncertainty principle is developed.…
Networks of genetic expression can be modelled by hypergraphs with the additional structure that real coefficients are given to each vertex-edge incidence. The spectra, i.e. the multiset of the eigenvalues, of such hypergraphs, are known to…
Biregular bipartite graphs have been proven to have similar edge distributions to random bipartite graphs and thus have nice pseudorandomness and expansion properties. Thus it is quite desirable to find a biregular bipartite spanning…
This is an exposition of results on the existence problem of $\pi_1$-injective immersed and embedded surfaces in graph-manifolds, and also of nonpositively curved metrics on graph-manifolds, obtained by different authors. The results are…
Graph Neural Networks (GNNs) are characterized by their capacity of processing graph-structured data. However, due to the sparsity of labels under semi-supervised learning, they have been found to exhibit biased performance on specific…
The utility of a matrix satisfying the Strong Spectral Property has been well established particularly in connection with the inverse eigenvalue problem for graphs. More recently the class of graphs in which all associated symmetric…
The interference imposes a significant negative impact on the performance of wireless networks. With the continuous deployment of larger and more sophisticated wireless networks, reducing interference in such networks is quickly being…
In this work, we propose to study the utility of different meta-graphs, as well as how to simultaneously leverage multiple meta-graphs for HIN embedding in an unsupervised manner. Motivated by prolific research on homogeneous networks,…
In recent years, spectral graph neural networks, characterized by polynomial filters, have garnered increasing attention and have achieved remarkable performance in tasks such as node classification. These models typically assume that…
A new family of graphs, {\it entangled networks}, with optimal properties in many respects, is introduced. By definition, their topology is such that optimizes synchronizability for many dynamical processes. These networks are shown to have…