Related papers: Spectral analysis of communication networks using …
We study $\Gamma$-convergence of graph Dirichlet energies and spectral convergence of graph Laplacians on unions of intersecting manifolds of potentially different dimensions. Our investigation is motivated by problems of machine learning,…
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…
We provide a simple proof that graphs in a general class of self-similar networks have zero percolation threshold. The considered self-similar networks include random scale-free graphs with given expected node degrees and zero clustering,…
The work in this thesis concerns the investigation of eigenvalues of the Laplacian matrix, normalized Laplacian matrix, signless Laplacian matrix and distance signless Laplacian matrix of graphs. In Chapter 1, we present a brief…
Quantum graphs and their experimental counterparts, microwave networks, are ideally suited to study the spectral statistics of chaotic systems. The graph spectrum is obtained from the zeros of a secular determinant derived from energy and…
It is reported that dynamical systems over digraphs have superior performance in terms of system damping and tolerance to time delays if the underlying graph Laplacian has a purely real spectrum. This paper investigates the topological…
We consider a random geometric graph with vertices sampled from a probability measure supported on $\mathbb R^d$, and study its connectivity. We show the graph is typically disconnected, unless the sampling density has superexponential…
Networks or graphs can easily represent a diverse set of data sources that are characterized by interacting units or actors. Social networks, representing people who communicate with each other, are one example. Communities or clusters of…
We study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices. We give a complete prescription for calculating the spectra that is exact in the limit…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
Let a graph be observed through a finite random sampling mechanism. Spectral methods are routinely applied to such graphs, yet their outputs are treated as deterministic objects. This paper develops finite-sample inference for spectral…
In this note, we study Laplacians on graphs for which connectivity within certain subgraphs tends to infinity. Our main focus are graphs sharing a common node set on which edge weights within certain clusters grow to infinity. As…
Consistency is a key property of all statistical procedures analyzing randomly sampled data. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of…
This paper uses the relationship between graph conductance and spectral clustering to study (i) the failures of spectral clustering and (ii) the benefits of regularization. The explanation is simple. Sparse and stochastic graphs create a…
Large graphs commonly appear in social networks, knowledge graphs, recommender systems, life sciences, and decision making problems. Summarizing large graphs by their high level properties is helpful in solving problems in these settings.…
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…
Network representations are useful for describing the structure of a large variety of complex systems. Although most studies of real-world networks suppose that nodes are connected by only a single type of edge, most natural and engineered…
The spectra of digraphs, unlike those of graphs, is a relatively unexplored territory. In a digraph, a separation is a pair of sets of vertices X and Y such that there are no arcs from X and Y . For a subclass of eulerian digraphs, we give…
Spectral clustering is a widely used algorithm to find clusters in networks. Several researchers have studied the stability of spectral clustering under local differential privacy with the additional assumption that the underlying networks…
We consider the problem of finding universal bounds of "isoperimetric" or "isodiametric" type on the spectral gap of the Laplacian on a metric graph with natural boundary conditions at the vertices, in terms of various analytical and…