The superscript H refers to the Hermitian transpose, which includes transposition and complex conjugation. That is, for any matrix A, AH = AT . An eigenvector of A, as defined above, is sometimes called a right eigenvector of A, to distinguish from a left eigenvector. It can be seen that if y is a left eigenvector of A with eigenvalue , then y is also a right eigenvector of AH , with eigenvalue...

We exhibit new functions of the eigenvectors Dyson Brownian motion which follow an equation similar to Bourgade-Yau eigenvector moment flow (Bourgade and Yau in Commun Math Phys 350(1):231–278, 2017). These observables can be seen as a Fermionic counterpart original (Bosonic) ones. By analyzing both Bosonic observables, we obtain correlations between eigenvectors: (i) The fluctuations $$\sum _{...

In this paper we propose a weighted multi-hypergraph as logical structure to model relationships between researchers and interest groups that join them on the base of shared research topics in a given scientific community. The well known concept of eingenvector centrality for graphs is extended to weighted multi-hypergraphs and we present a model instantiation for centrality analysis in the Pro...

We use the susceptible-infected-recovered (SIR) model for disease spread over a network, and empirically study how well various centrality measures perform at identifying which nodes in a network will be the best spreaders of disease on 10 real-world networks. We find that the relative performance of degree, shell number and other centrality measures can be sensitive to β , the probability that...

The goal of this paper is to present a centrality measurement for the nodes of a hypergraph, by using existing literature which extends eigenvector centrality from a graph to a hypergraph, and literature which give a general centrality measurement for a graph. We’ll use this measurement to say more about the number of communications in a hypergraph, to implement a learning mechanism, and to con...

Viral marketing can be an effective marketing technique in social networks. Initiating from a set of influential seed users, it can activate a ‘‘chain-reaction’’ driven by word-of-mouth. The effectiveness of viral marketing lies in the fact that it conveys an implied endorsement from social ties. Existing approaches to selecting influential seeds depend on measures of global centrality within t...

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We prove convergence for the basic LR algorithm on a real unreduced tridiagonal matrix with a one-point spectrum the Jordan form is one big Jordan block. First we develop properties of eigenvector matrices. We also show how to deal with the singular case.

Eigenvector continuation is a computational method that finds the extremal eigenvalues and eigenvectors of Hamiltonian matrix with one or more control parameters. It does this by projection onto subspace corresponding to selected training values The has proven be very efficient accurate for interpolating extrapolating eigenvectors. However, almost nothing known about how converges, its rapid co...