Related papers: The Cheeger constant of a quantum graph
We study the eigenvalues of the connection Laplacian on a graph with an orthogonal group or unitary group signature. We establish higher order Buser type inequalities, i.e., we provide upper bounds for eigenvalues in terms of Cheeger…
We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits.
In this paper, we determine a formula for Kemeny's constant for a graph with multiple bridges, in terms of quantities that are inherent to the subgraphs obtained upon removal of all bridges and that can be computed independently. With the…
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…
We clarify the correspondence between the two approaches to quantum graphs: via quantum adjacency matrices and via quantum relations. We show how the choice of a (possibly non-tracial) weight manifests itself on the quantum relation side…
Cheeger-type inequalities in which the decomposability of a graph and the spectral gap of its Laplacian mutually control each other play an important role in graph theory and network analysis, in particular in the context of expander…
We introduce a family of multi-way Cheeger-type constants $\{h_k^{\sigma}, k=1,2,\ldots, n\}$ on a signed graph $\Gamma=(G,\sigma)$ such that $h_k^{\sigma}=0$ if and only if $\Gamma$ has $k$ balanced connected components. These constants…
A voltage graph is a finite directed graph whose edges are labeled by elements of a finite group $G$. A classical construction of Gross and Tucker associates to every voltage graph with vertex set $V$ a so-called derived graph with vertex…
The quantum graph plays the role of a solvable model for a two-dimensional network. Here fitting parameters of the quantum graph for modelling the junction is discussed, using previous results of the second author.
In the broad range of studies related to quantum graphs, quantum graph spectra appear as a topic of special interest. They are important in the context of diffusion type problems posed on metric graphs. Theoretical findings suggest that…
A factor-graph representation of quantum-mechanical probabilities is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not random variables.
The higher-order Cheeger inequalities were established for graphs by Lee, Oveis Gharan and Trevisan. We prove analogous inequalities for graphons in this article.
For discrete weighted graphs there is sufficient literature about the Cheeger cut and the Cheeger problem, but for metric graphs there are few results about these problems. Our aim is to study the Cheeger cut and the Cheeger problem in…
We introduce a new approach to confusability in a quantum channel, namely quantum confusability multigraph, which incorporates the output information into the graphical structure. By``counting" the edges between two vertices of this…
Some very elementary ideas about quantum groups and quantum algebras are introduced and a few examples of their physical applications are mentioned.
Transformers are increasingly employed for graph data, demonstrating competitive performance in diverse tasks. To incorporate graph information into these models, it is essential to enhance node and edge features with positional encodings.…
Studying the spectral theory of Schroedinger operator on metric graphs (also known as quantum graphs) is advantageous on its own as well as to demonstrate key concepts of general spectral theory. There are some excellent references for this…
We provide a quantitative lower bound to the Cheeger constant of a set $\Omega$ in both the Euclidean and the Gaussian settings in terms of suitable asymmetry indexes. We provide examples which show that these quantitative estimates are…
Quantum theory has shown its superiority in enhancing machine learning. However, facilitating quantum theory to enhance graph learning is in its infancy. This survey investigates the current advances in quantum graph learning (QGL) from…
Graph states form a rich class of entangled states that exhibit important aspects of multi-partite entanglement. At the same time, they can be described by a number of parameters that grows only moderately with the system size. They have a…