Related papers: Comparing large-scale graphs based on quantum prob…
This paper generalizes and unifies the existing spectral bounds on the $k$-independence number of a graph, which is the maximum size of a set of vertices at pairwise distance greater than $k$. The previous bounds known in the literature…
The newly introduced neighborhood matrix extends the power of adjacency and distance matrices to describe the topology of graphs. The adjacency matrix enumerates which pairs of vertices share an edge and it may be summarized by the degree…
Graphs are used in almost every scientific discipline to express relations among a set of objects. Algorithms that compare graphs, and output a closeness score, or a correspondence among their nodes, are thus extremely important. Despite…
We introduce two spectral invariants of finite metric spaces, the $q$-spectrum and the transition $q$-spectrum, defined from similarity matrices. These invariants extend the adjacency and Laplacian spectra of graphs to general finite metric…
Graph operations or products play an important role in complex networks. In this paper, we study the properties of $q$-subdivision graphs, which have been applied to model complex networks. For a simple connected graph $G$, its…
We explore algebraic and spectral properties of weighted graphs containing twin vertices that are useful in quantum state transfer. We extend the notion of adjacency strong cospectrality to arbitrary Hermitian matrices, with focus on the…
In this paper, we propose a new spectral-based approach to hypothesis testing for populations of networks. The primary goal is to develop a test to determine whether two given samples of networks come from the same random model or…
We introduce new distance measures for comparing straight-line embedded graphs based on the Fr\'echet distance and the weak Fr\'echet distance. These graph distances are defined using continuous mappings and thus take the combinatorial…
Let $D(G)$ denote the distance matrix of a connected graph $G$ with $n$ vertices. The distance spectral gap of a graph $G$ is defined as $\delta_{D^G} = \rho_1 - \rho_2$, where $\rho_1$ and $\rho_2$ represent the largest and second largest…
In the present paper, we study the continuous-time quantum walk on quotient graphs. On such graphs, there is a straightforward reduction of problem to a subspace that can be considerably smaller than the original one. Along the lines of…
A distance measure is presented between two unitary propagators of quantum systems of differing dimensions along with a corresponding method of computation. A typical application is to compare the propagator of the actual (real) process…
This paper introduces a simple measure of a concordance pattern among observed outcomes along a network, i.e., the pattern in which adjacent outcomes tend to be more strongly correlated than non-adjacent outcomes. The graph concordance…
A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…
In this paper we present a general procedure that allows for the reduction or expansion of any network (considered as a weighted graph). This procedure maintains the spectrum of the network's adjacency matrix up to a set of eigenvalues…
A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph into a large network. We propose two complementary MCMC algorithms for…
Let $G=(V,E)$ be a $d$-regular graph on $n$ vertices and let $\mu_0$ be a probability measure on $V$. The act of moving to a randomly chosen neighbor leads to a sequence of probability measures supported on $V$ given by $\mu_{k+1} = A…
Distances between probability distributions are a key component of many statistical machine learning tasks, from two-sample testing to generative modeling, among others. We introduce a novel distance between measures that compares them…
We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…
Graphs with large spectral gap are important in various fields such as biology, sociology and computer science. In designing such graphs, an important question is how the probability of graphs with large spectral gap behaves. A method based…
We set the ground for a theory of quantum walks on graphs- the generalization of random walks on finite graphs to the quantum world. Such quantum walks do not converge to any stationary distribution, as they are unitary and reversible.…