Fandom

VroniPlag Wiki

Quelle:Nm2/Koschuetzki et al 2005

< Quelle:Nm2

31.340Seiten in
diesem Wiki
Seite hinzufügen
Diskussion0

Störung durch Adblocker erkannt!


Wikia ist eine gebührenfreie Seite, die sich durch Werbung finanziert. Benutzer, die Adblocker einsetzen, haben eine modifizierte Ansicht der Seite.

Wikia ist nicht verfügbar, wenn du weitere Modifikationen in dem Adblocker-Programm gemacht hast. Wenn du sie entfernst, dann wird die Seite ohne Probleme geladen.

Angaben zur Quelle [Bearbeiten]

Autor     D. Koschützki, K.A. Lehmann, L. Peeters, S. Richter, D. Tenfelde- Podehl, O. Zlotowski
Titel    Chapter 3 Centrality Indices
Sammlung    Network Analysis: Methodological Foundations
Herausgeber    Ulrik Brandes, Thomas Erlebach
Ort    Berlin Heidelberg
Verlag    Springer
Jahr    2005
Seiten    16-61
ISBN    978-3-540-24979-5
ISSN    0302-9743
URL    http://books.google.de/books?id=TTNhSm7HYrIC

Literaturverz.   

no
Fußnoten    no
Fragmente    3


Fragmente der Quelle:
[1.] Nm2/Fragment 436 05 - Diskussion
Zuletzt bearbeitet: 2014-01-11 22:28:47 WiseWoman
Fragment, Gesichtet, KomplettPlagiat, Koschuetzki et al 2005, Nm2, SMWFragment, Schutzlevel sysop

Typus
KomplettPlagiat
Bearbeiter
Hindemith
Gesichtet
Yes.png
Untersuchte Arbeit:
Seite: 436, Zeilen: 5-11
Quelle: Koschuetzki et al 2005
Seite(n): 20, Zeilen: 8-16
The degree centrality Cd(v) of a vertex v is simply defined as the degree d(v) of v if the considered graph is undirected. The degree centrality is, e.g., applicable whenever the graph represents something like a voting result. These networks represent a static situation and we are interested in the vertex that has the most direct votes or that can reach most other vertices directly. The degree centrality is a local measure, because the centrality value of a vertex is only determined by the number of its neighbors. The most simple centrality is the degree centrality cD(v) of a vertex v that is simply defined as the degree d(v) of v if the considered graph is undirected. [...] The degree centrality is, e.g., applicable whenever the graph represents something like a voting result. These networks represent a static situation and we are interested in the vertex that has the most direct votes or that can reach most other vertices directly. The degree centrality is a local measure, because the centrality value of a vertex is only determined by the number of its neighbors.
Anmerkungen

The source is not mentioned anywhere in the paper.

Sichter
(Hindemith), WiseWoman

[2.] Nm2/Fragment 436 28 - Diskussion
Zuletzt bearbeitet: 2014-01-12 10:20:16 Singulus
Fragment, Gesichtet, Koschuetzki et al 2005, Nm2, SMWFragment, Schutzlevel sysop, Verschleierung

Typus
Verschleierung
Bearbeiter
Hindemith
Gesichtet
Yes.png
Untersuchte Arbeit:
Seite: 436, Zeilen: 28-39
Quelle: Koschuetzki et al 2005
Seite(n): 22, 23, Zeilen: 22: 12ff; 23: 1-3
We denote the sum of the distances from a vertex u ∈ V to any other vertex in a graph G = (V,E) as the total distance \sum_{u\in V}d(u,v), where d(u,v) is shortest [sic] distance between the nodes u and v The problem of finding an appropriate location can be solved by computing the set of vertices with minimum total distance.

In SNA literature, a centrality measure based on this concept is called closeness. The focus lies here, for example, on measuring the closeness of a person to all other people in the network. People with a small total distance are considered as most important as those with high total distance. The most commonly employed definition of closeness is the reciprocal of the total distance:

C_{C}(u)=\frac{1}{\sum_{v\in V}d(u,v)}\qquad (2)

C_{C}(u) grows with decreasing total distance of u, therefore it is also known as a structural index.

We denote the sum of the distances from a vertex u ∈ V to any other vertex in a graph G = (V,E) as the total distance2 \sum_{v\in V}d(u,v). The problem of finding an appropriate location can be solved by computing the set of vertices with minimum total distance. [...]

In social network analysis a centrality index based on this concept is called closeness. The focus lies here, for example, on measuring the closeness of a person to all other people in the network. People with a small total distance are considered as more important as those with a high total distance. [...] The most commonly employed definition of closeness is the reciprocal of the total distance

[page 23]

C_{C}(u)=\frac{1}{\sum_{v\in V}d(u,v)}\qquad (3.2)

In our sense this definition is a vertex centrality, since 'C_{C}(u) grows with decreasing total distance of u and it is clearly a structural index.


2 In [273], Harary used the term status to describe a status of a person in an organization or a group. In the context of communication networks this sum is also called transmission number.

Anmerkungen

The source is not mentioned anywhere in the paper.

Sichter
(Hindemith), WiseWoman

[3.] Nm2/Fragment 437 09 - Diskussion
Zuletzt bearbeitet: 2014-01-12 10:23:42 Singulus
Fragment, Gesichtet, Koschuetzki et al 2005, Nm2, SMWFragment, Schutzlevel sysop, Verschleierung

Typus
Verschleierung
Bearbeiter
Hindemith
Gesichtet
Yes.png
Untersuchte Arbeit:
Seite: 437, Zeilen: 9-19
Quelle: Koschuetzki et al 2005
Seite(n): 29-30, Zeilen: 29: 26ff; 30: 1, 13-15
Let \delta_{uw}(v) denotes the fraction of shortest paths between u and w that contain vertex v:

\delta_{uw}(v)=\frac{\sigma_{uw}(v)}{\sigma_{uw}}\quad (3)

where \sigma_{uw} denotes the number of all shortest-paths between u and w. The ratio \delta_{uw}(v) can be interpreted as the probability that vertex v is involved into any communication between u and w. Note, that the measure implicitly assumes that all communication is conducted along shortest paths. Then the betweenness centrality C_{B}(v) of a vertex v is given by:

C_{B}(v)=\sum_{u\neq v\in V}\sum_{w\neq v\in V}\delta_{uw}(v)\quad (4)

Any pair of vertices u and w without any shortest path from u to w will add zero to the betweenness centrality of every other vertex in the network.

Let \delta_{st}(v) denote the fraction of shortest paths between s and t that contain vertex v:

\delta_{st}(v)=\frac{\sigma_{st}(v)}{\sigma_{st}}\quad (3.12)

where \sigma_{st} denotes the number of all shortest-path [sic] between s and t. Ratios \delta_{st}(v) can be interpreted as the probability that vertex v is involved into any communication between s and t. Note, that the index implicitly assumes that all communication is conducted along shortest paths. Then the betweenness centrality c_{B}(v) of a vertex v is given by:

[page 30]

c_{B}(v)=\sum_{s\neq v\in V}\sum_{t\neq v\in V}\delta_{st}(v)\quad (3.13)

[...]

Any pair of vertices s and t without any shortest path from s to t just will add zero to the betweenness centrality of every other vertex in the network.

Anmerkungen

The definitions given here are, of course, standard and don't require a citation. However, the interpreting and explaining text is taken from the source word for word. The source is not mentioned in the paper anywhere.

Sichter
(Hindemith), WiseWoman

Auch bei Fandom

Zufälliges Wiki