Related papers: Subdivision method in the Laplacian matching polyn…

We study finite graphs embedded in oriented surfaces by associating a polynomial to it. The tools used in developing a theory of such graph polynomials are algebraic topological while the polynomial itself is inspired from ideas arising in…

Symmetry plays a major role in subgraph matching both in the description of the graphs in question and in how it confounds the search process. This work addresses how to quantify these effects and how to use symmetries to increase the…

This paper tackles the challenging problem of jointly inferring time-varying network topologies and imputing missing data from partially observed graph signals. We propose a unified non-convex optimization framework to simultaneously…

Graph-based methods play an important role in unsupervised and semi-supervised learning tasks by taking into account the underlying geometry of the data set. In this paper, we consider a statistical setting for semi-supervised learning and…

It is conjectured that the Laplacian spectrum of a graph is majorized by its conjugate degree sequence. In this paper, we prove that this majorization holds for a class of graphs including trees. We also show that a generalization of this…

A popular approach to semi-supervised learning proceeds by endowing the input data with a graph structure in order to extract geometric information and incorporate it into a Bayesian framework. We introduce new theory that gives appropriate…

Graph connection Laplacian (GCL) is a modern data analysis technique that is starting to be applied for the analysis of high dimensional and massive datasets. Motivated by this technique, we study matrices that are akin to the ones…

A new approach of graph matching is introduced in this paper, which efficiently solves the problem of graph isomorphism and subgraph isomorphism. In this paper we are introducing a new approach called SubGraD, for query graph detection in…

In this paper we propose a graph superalgebra which is the supersymmetric analogue of Leavitt path algebras. We find a basis for these superalgebras and characterize when they have polynomial growth.

A stationary subdivision scheme generates the full space of polynomials of degree up to $k$ if and only if its mask satisfies sum rules of order $k+1$, or its symbol satisfies zero conditions of order $k+1$. This property is often called…

Consider any random graph model where potential edges appear independently, with possibly different probabilities, and assume that the minimum expected degree is omega(ln n). We prove that the adjacency matrix and the Laplacian of that…

In this article, we develop a perturbative technique to construct families of non-isomorphic discrete graphs which are isospectral for the standard (also called normalised) Laplacian and its signless version. We use vertex contractions as a…

Graph-based semi-supervised learning usually involves two separate stages, constructing an affinity graph and then propagating labels for transductive inference on the graph. It is suboptimal to solve them independently, as the correlation…

The Laplacian matrix and its pseudo-inverse for a strongly connected directed graph is fundamental in computing many properties of a directed graph. Examples include random-walk centrality and betweenness measures, average hitting and…

This article describes an implementation of a nonparametric Bayesian approach to solving binary classification problems on graphs. We consider a hierarchical Bayesian approach with a prior that is constructed by truncating a series…

Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…

The bipartition polynomial of a graph is a generalization of many other graph polynomials, including the domination, Ising, matching, independence, cut, and Euler polynomial. We show in this paper that it is also a powerful tool for proving…

Recently normalized Laplacian matrices of graphs are studied as density matrices in quantum mechanics. Separability and entanglement of density matrices are important properties as they determine the nonclassical behavior in quantum…

We study entanglement properties of mixed density matrices obtained from combinatorial Laplacians. This is done by introducing the notion of the density matrix of a graph. We characterize the graphs with pure density matrices and show that…

Graph disaggregation is a technique used to address the high cost of computation for power law graphs on parallel processors. The few high-degree vertices are broken into multiple small-degree vertices, in order to allow for more efficient…