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Extra info for Analysis of Asymmetric Communication Patterns in Computer Mediated Communication Environments
Closeness centrality gives an indication of how close a member is to the other members of the group. This can intuitively be derived from the distances between vertex ✰ and all other members. It should be mentioned though that if the actor is an isolate, 20 CHAPTER 3 meaning, that he has no connections at all, the sum of distances becomes ✳ and thus the index is undefined. ) puts the focus on the fact that a vertex ✚ with a Betweenness centrality ✉✈❛ ☎ ✛ high betweenness centrality is like a bottleneck.
The distribution of the eigenvector components within each eigenvector looses its star like characteristic. The anchor is still visible, but the behavior of the other vertices changes. 4) In addition it can be said, that if one reverses the direction of the edge between two vertices, the eigenvalues are kept, but the eigenvectors become complex conjugated. 5). 6)). 13 ❧♦ ❦ ❤❜ ❝ ❣❥ ♦ ❜❝ ❣❱❤ ❧♥ ❦ ❤❜ ❝ ❣❥ ♥ ❜❝ ❞ ❣❱❤ ❛❜ ❝ ❧ ♠ ❜❦ ❝ ❤ ❣❥ ♠ ❜❝ ❣❤ ❧✐ ❦ ❤ ❜❳❝ ❣❥ ✐ ❜❝ ❣❤ 1 2 3 4 52 CHAPTER 4 CHAPTER 4 53 The eigensystem also indicates the location of the perturbing event.
1 Degree based Rank In this subsection the rank based on in- or out-degree will be described. Thus an intuitive introduction to the concept of rank is given even though the proposed method is not restricted to degree centrality. Degree in this context when directed weighted graphs are observed is the number of edges ✜ that either depart from a vertex ✚ (out-degree: ✷✆☎❪ ✛ ) or are pointed towards the vertex (in-degree: ☎ ✷✆❫ ✛ ). In the case of weighted graphs we also define the strength following Barrat et al.