By Bettina Hoser
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62) ✗ with representing a ▼øÏ➔ matrix. In general, this is the representation of a bipartite graph. In the special case of n=1 and m=k this matrix represents a directed, weighted star graph with ✰ ➑ ✲ vertices. 63) ➧ ❁➛ ➛❁➛ ❦ ⑩ ❋ ❜ ✾ ❦ ⑩ ❋ ❜ ☞✤ ❢♥✤ ☞✤ ☞ ☞ ⑩ ❜ ✤ , ✤ ➧ ✤ ❅ ✤ ⑩ ❜ ❢♥✤ , etc. ❅ (see [Mey00, p. 555]) with ❋ ❋ ✾ The eigenvalues are by definition of the same absolute value, but being the ✗ square roots of the singular values of they have either sign. For the respective eigenvectors this leads to the fact that they are only determined up to multiples of ✃ .
2: Communication behavior after rotation 4. 1) behave under rotation. Note that the norm is invariant under rotation. The absolute value - that is the representation of the amount of of communication - does not change. 2 will be discussed. In 46 CHAPTER 4 ✬ ☞ ✠ the following the solution of the eigensystem ✠ ❅ is considered. 2, the interpretation of eigenvectors and the resulting orthogonal projectors will be explained. 42). Thus changes with the number of ☞ messages exchanged. does not reveal if the number of in- or outbound messages has changed.
1) ✝❡❞❣❢✐❤ ❘ ✳ and ☎✞✝ ❅✽✳ if ✄✆☎✞✝ ❅✽✳ . 2) In the weighted case it is not possible to standardize anymore, since the number of possible connections is no longer known. In that case just the row sum is taken. This then has the problem of comparability between networks. ) Strength is the concept in the weighted case. 3). It is given as the row sum of the weighted adjacency matrix divided by the total sum of matrix entries, with ✄✆☎✞✝ ✛ and ▼ the number of vertices or members in the network. 3) ♦ ♦ There are several derived concepts of centrality which will be presented without further explanation.
Analysis of Asymmetric Communication Patterns in Computer Mediated Communication Environments by Bettina Hoser