Among the many centrality indices used to detect structures of actors’ positions in networks is the use of the first eigenvector of an adjacency matrix that captures the connections among the actors. This research considers the seeming pervasive current practice of using only the first eigenvector. It is shows that, as in other statistical applications of eigenvectors, subsequent vectors can al...

In a paper examining informal networks and organizational crisis, Krackhardt and Stern (1988) proposed a measure assessing the extent to which relations in a network were internal to a group as opposed to rokerage roles ategorical attributes external. They called their measure the E–I index. The measure is now in wide use and is implemented in standard network packages such as UCINET (Borgatti ...

Abstract We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on eigenvector, or several eigenvectors (or their corresponding invariant subspace). The are derived from an implicit viewpoint. More precisely, we change Newton update equation in a way that next iterate does not only appear linearly equation. Although modifications of make methods implic...

Eigenvector localization refers to the situation when most of the components of an eigenvector are zero or near-zero. This phenomenon has been observed on eigenvectors associated with extremal eigenvalues, and in many of those cases it can be meaningfully interpreted in terms of “structural heterogeneities” in the data. For example, the largest eigenvectors of adjacency matrices of large comple...

We study the lobby index ( l for short) as a local node centrality measure for complex networks. The l is compared with degree (a local measure), betweenness and Eigenvector centralities (two global measures) in the case of a biological network (Yeast interaction protein-protein network) and a linguistic network (Moby Thesaurus II ). In both networks, the l has poor correlation with betweenness...

This paper proposes a novel pre-FFT type OFDM adaptive array antenna called “Eigenvector Combining.” The eigenvector combining array antenna is a realization of a post-FFT type OFDM adaptive array antenna through a pre-FFT signal processing, so it can achieve excellent performance with less computational complexity and shorter training symbols. Numerical results demonstrate that the proposed ei...

2.1 Computing Eigenvectors from the Characteristic Polynomial The characteristic polynomial can be used to develop an algorithm for computing the eigenvectors and eigenvalues. This algorithm, which is known as Power Iteration, takes advantage of the property that vectors which are transformed by the matrix A will be scaled in the direction of the largest eigenvector. Initially, the vector is ch...

We develop majorisation results that characterise changes in eigenvector components of a graph’s adjacency matrix when its topology is changed. Specifically, for general (weighted, directed) graphs, we characterise changes in dominant eigenvector components for singleand multi-row incrementations. We also show that topology changes can be tailored to set ratios between the components of the dom...