Related papers: Self-testing graph states
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
Locally-biased graph algorithms are algorithms that attempt to find local or small-scale structure in a large data graph. In some cases, this can be accomplished by adding some sort of locality constraint and calling a traditional graph…
Let $\mathcal{V}$ and $\mathcal{U}$ be the point sets of two independent homogeneous Poisson processes on $\mathbb{R}^d$. A graph $\mathcal{G}_\mathcal{V}$ with vertex set $\mathcal{V}$ is constructed by first connecting pairs of points…
Graphs provide a powerful representation formalism that offers great promise to benefit tasks like handwritten signature verification. While most state-of-the-art approaches to signature verification rely on fixed-size representations,…
We give a criterion that is sufficient for controllability of multipartite quantum systems. We generalize the graph infection criterion to the quantum systems that cannot be described with the use of a graph theory. We introduce the…
Self-testing refers to a method with which a classical user can certify the state and measurements of quantum systems in a device-independent way. Especially, the self-testing of entangled states is of great importance in quantum…
Given a locally finite simple graph so that its degree is not bounded, every self-adjoint realization of the adjacency matrix is unbounded from above. In this note we give an optimal condition to ensure it is also unbounded from below. We…
The class of entangled $N$-qubit states known as graph states, and the corresponding stabilizer groups of $N$-qubit Pauli observables, have found a wide range of applications in quantum information processing and the foundations of quantum…
Modeling how networks change under structural perturbations can yield foundational insights into network robustness, which is critical in many real-world applications. The largest connected component is a popular measure of network…
In this article we discuss general strategies and computer algorithms to test the connectivity of unstructured networks which consist of a number of segments connected through randomly distributed nodes.
How can researchers test for heterogeneity in the local structure of a network? In this paper, we present a framework that utilizes random sampling to give subgraphs which are then used in a goodness of fit test to test for heterogeneity.…
A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…
We study a class of graphs that represent local independence structures in stochastic processes allowing for correlated error processes. Several graphs may encode the same local independencies and we characterize such equivalence classes of…
An automorphism on a graph $G$ is a bijective mapping on the vertex set $V(G)$, which preserves the relation of adjacency between any two vertices of $G$. An automorphism $g$ fixes a vertex $v$ if $g$ maps $v$ onto itself. The stabilizer of…
Property Testing is a formal framework to study the computational power and complexity of sampling from combinatorial objects. A central goal in standard graph property testing is to understand which graph properties are testable with…
The Ramsey's theorem says that a graph with sufficiently many vertices contains a clique or stable set with many vertices. Now we attach some parameter to every vertex, such as degree. Consider the case a graph with sufficiently many…
We study the problem of testing conductance in the setting of distributed computing and give a two-sided tester that takes $\mathcal{O}(\log(n) / (\epsilon \Phi^2))$ rounds to decide if a graph has conductance at least $\Phi$ or is…
We introduce a technique called graph fission which takes in a graph which potentially contains only one observation per node (whose distribution lies in a known class) and produces two (or more) independent graphs with the same node/edge…
Let $G=(V,E)$ be a simple graph. A set $I\subseteq V$ is an independent set, if no two of its members are adjacent in $G$. The $k$-independent graph of $G$, $I_k (G)$, is defined to be the graph whose vertices correspond to the independent…
We create the unlabeled or vertex-labeled graphs with up to 10 edges and up to 10 vertices and classify them by a set of standard properties: directed or not, vertex-labeled or not, connectivity, presence of isolated vertices, presence of…