This paper describes a spectral method for graphmatching. We adopt a graphical models viewpoint in which the graph adjacency matrix is taken to represent the transition probability matrix of a Markov chain. The node-order of the steady state random walk associated with this Markov chain is determined by the co-efficent order of the leading eigenvector of the adjacency matrix. We match nodes in ...

The n × n Brualdi-Li matrix Bn has recently been shown to have maximal Perron value (spectral radius) ρ among all tournament matrices of even order n, thus settling the conjecture by the same name. This renews our interest in estimating ρ and motivates us to study the Perron eigenvector x of Bn, which is normalized to have 1-norm equal to one. It follows that x minimizes the 2-norm among all Pe...

The centrality of an agent in a network has been shown to be crucial in explaining different behaviors and outcomes. In this paper, we propose an axiomatic approach to characterize centrality measures for which the centrality of an agent is recursively related to the centralities of the agents she is connected to. This includes the Katz-Bonacich and the eigenvector centrality. The core of our a...

A fast eigenvector technique for obtaining good initial node partitions of netlists for use in interchange heuristics is described. The method is based on approximating the netlist or hypergraph by a weighted graph, G, such that the sum of the cut edges in G tightly underestimates the number of cut nets in any netlist partition. An eigenvector technique of Barnes [2] is used to partition the gr...

The influence of catechol-o-methyltransferase (COMT) Val(158)Met on brain activation and functional connectivity has been widely reported. However, voxel-wise effects of this genotype on resting-state brain networks remain unclear. Here, we used resting-state fMRI and eigenvector centrality to examine the effects of COMT Val(158)Met genotypes on the connection patterns of the brain network and ...

Eigenvector-based methods such as multiple signal classification (MUSIC) are currently popular in sinusoidal frequency estimation due to their high resolution. A problem with these methods is the often high cost of estimating the eigenvectors of the autocorrelation matrix spanning the signal (or noise) subspace. In this work, we propose an efficient Fourier transform-based method avoiding eigen...

Boolean networks serve as discrete models of regulation and signaling in biological cells. Identifying the key controllers of such processes is important for understanding the dynamical systems and planning further analysis. Here we quantify the dynamical impact of a node as the probability of damage spreading after switching the node’s state. We find that the leading eigenvector of the adjacen...

Eigenvalue spectrum of adjacency matrices of many complex networks reveals that a large real eigenvalue separate from the bulk of the population of eigenvalues. A related theorem in this observation is that of Perron-Frobenius, which states that ifˆA is a positive matrix, then there exists a unique eigenvalue ofˆA, which has the greatest absolute value, and its associated eigenvector may be tak...

Broadband adaptive beamformers, which use a narrowband SNRmaximization optimization criterion for noise reduction, typically cause distortions of the desired speech signal at the beamformer output. In this paper two methods are investigated to control the speech distortion by comparing the eigenvector beamformer with a maximum likelihood beamformer: One is an analytic solution for the ideal cas...