By Bettina Hoser

ISBN-10: 393730049X

ISBN-13: 9783937300498

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In this case for example one sided communication or very little communication between two nodes takes the form of a perturbation. 2 Eigenvectors and orthogonal projectors The absolute value of the eigenvector components is the well known eigenvector centrality index (see Bonacich and Lloyd [BL01]). In this context this index can be interpreted as a similarity in communication pattern among the group members. Thus the component with highest absolute value can be interpreted as the highest ranked member within that pattern.

With these bounds it would be possible to check if and how a matrix is ✔ the result of a perturbation . This will be of some interest in chapter 4, when the construction and behavior of complex Hermitian adjacency matrices and their ✬ respective eigensystems will be discussed. Since a Hermitian matrix can be represented by a Fourier sum of its subspaces, the addends, ordered by their weights (the corresponding eigenvalues) can be seen as an approximation of a perturbation. The addend with a relative high weight can be seen as the unperturbed matrix, with all other addends as perturbation matrices.

13 ❧♦ ❦ ❤❜ ❝ ❣❥ ♦ ❜❝ ❣❱❤ ❧♥ ❦ ❤❜ ❝ ❣❥ ♥ ❜❝ ❞ ❣❱❤ ❛❜ ❝ ❧ ♠ ❜❦ ❝ ❤ ❣❥ ♠ ❜❝ ❣❤ ❧✐ ❦ ❤ ❜❳❝ ❣❥ ✐ ❜❝ ❣❤ 1 2 3 4 52 CHAPTER 4 CHAPTER 4 53 The eigensystem also indicates the location of the perturbing event.

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Analysis of Asymmetric Communication Patterns in Computer Mediated Communication Environments by Bettina Hoser

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