Related papers: Spectra of random graphs with arbitrary expected d…
We introduce and analyse ensembles of 2-regular random graphs with a tuneable distribution of short cycles. The phenomenology of these graphs depends critically on the scaling of the ensembles' control parameters relative to the number of…
This paper revisits the classical concept of network modularity and its spectral relaxations used throughout graph data analysis. We formulate and study several modularity statistic variants for which we establish asymptotic distributional…
The eccentricity matrix of a connected graph $G$ is obtained from the distance matrix of $G$ by retaining the largest distances in each row and each column, and setting the remaining entries as $0$. In this article, a conjecture about the…
The spectrum of a graph is closely related to many graph parameters. In particular, the spectral gap of a regular graph which is the difference between its valency and second eigenvalue, is widely seen an algebraic measure of connectivity…
In graph signal processing, the graph adjacency matrix or the graph Laplacian commonly define the shift operator. The spectral decomposition of the shift operator plays an important role in that the eigenvalues represent frequencies and the…
We investigate the spectrum of the non-backtracking matrix of a graph. In particular, we show how to obtain eigenvectors of the non-backtracking matrix in terms of eigenvectors of a smaller matrix. Furthermore, we find an expression for the…
We study regular graphs whose distance-$2$ graph or distance-$1$-or-$2$ graph is strongly regular. We provide a characterization of such graphs $\Gamma$ (among regular graphs with few distinct eigenvalues) in terms of the spectrum and the…
The purpose of this paper is to analyze the degree index and clustering index in random graphs. The degree index in our setup is a certain measure of degree irregularity whose basic properties are well studied in the literature, and the…
Graph vertex sampling set selection aims at selecting a set of ver-tices of a graph such that the space of graph signals that can be reconstructed exactly from those samples alone is maximal. In this context, we propose to extend sampling…
We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size…
Arrangement graphs were introduced for their connection to computational networks and have since generated considerable interest in the literature. In a pair of recent articles by Chen, Ghorbani and Wong, the eigenvalues for the adjacency…
We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…
In this thesis, which is supervised by Dr. David Penman, we examine random interval graphs. Recall that such a graph is defined by letting $X_{1},\ldots X_{n},Y_{1},\ldots Y_{n}$ be $2n$ independent random variables, with uniform…
We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…
This paper surveys some recent results and progress on the extremal prob- lems in a given set consisting of all simple connected graphs with the same graphic degree sequence. In particular, we study and characterize the extremal graphs…
We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the…
We analyse growing networks ranging from collaboration graphs of scientists to the network of similarities defined among the various transcriptional profiles of living cells. For the explicit demonstration of the scale-free nature and…
Determining and analyzing the spectra of graphs is an important and exciting research topic in theoretical computer science. The eigenvalues of the normalized Laplacian of a graph provide information on its structural properties and also on…
Generative models for graphs have been typically committed to strong prior assumptions concerning the form of the modeled distributions. Moreover, the vast majority of currently available models are either only suitable for characterizing…
We completely determine the spectrum of an $I$-graph, that is, the eigenvalues of its adjacency matrix. We apply our result to prove known characterizations of connectedness and bipartiteness in $I$-graphs by using an spectral approach.…