Quelle:Nm/Brandes Erlebach 2005

Angaben zur Quelle [Bearbeiten]

Autor	Ulrik Brandes, Thomas Erlebach
Titel	Chapter 2 Fundamentals
Sammlung	Network Analysis: Methodological Foundations
Herausgeber	Ulrik Brandes, Thomas Erlebach
Ort	Berlin Heidelberg
Verlag	Springer
Jahr	2005
ISBN	978-3-540-24979-5
ISSN	0302-9743
URL	http://www.inf.uni-konstanz.de/algo/publications/be-f-05.pdf
Literaturverz.	no
Fußnoten	no
Fragmente	3

Fragmente der Quelle:

[1.] Nm/Fragment 097 09 - Diskussion
Zuletzt bearbeitet: 2012-04-26 07:59:44 Fiesh

Brandes Erlebach 2005, Fragment, Gesichtet, Nm, SMWFragment, Schutzlevel sysop, Verschleierung

Typus: Verschleierung

Bearbeiter: Hindemith

Gesichtet

Untersuchte Arbeit:
Seite: 97, Zeilen: 9-19

Quelle: Brandes_Erlebach_2005
Seite(n): 7, 8, Zeilen: p7: 30ff; p8: 1ff

Graphs can be undirected or directed. The adjacency matrix of an undirected graph (as shown in Figure 3.2) is symmetric. An undirected edge joining vertices 
  
        u
        ,
        v
        ∈
        V
      
    {\displaystyle u, v \in V}
  
 is denoted by 
  
        {
        u
        ,
        v
        }
      
    {\displaystyle \{u, v\}}
  
.
In directed graphs, each directed edge (arc) has an origin (tail) and a destination (head). An edge with origin 
  
        u
        ∈
        V
      
    {\displaystyle u \in V}
  
 is represented by an order pair 
  
        (
        u
        ,
        v
        )
      
    {\displaystyle (u, v)}
  
. As a shorthand notation, an edge 
  
        {
        u
        ,
        v
        }
      
    {\displaystyle \{u, v\}}
  
 can also be denoted by 
  
        u
        v
      
    {\displaystyle uv}
  
. It is to note that, in a directed graph, 
  
        u
        v
      
    {\displaystyle uv}
  
 is short for 
  
        (
        u
        ,
        v
        )
      
    {\displaystyle (u, v)}
  
, while in an undirected graph, 
  
        u
        v
      
    {\displaystyle uv}
  
 and 
  
        v
        u
      
    {\displaystyle vu}
  
 are the same and both stands for 
  
        {
        u
        ,
        v
        }
      
    {\displaystyle \{u, v\}}
  
. Graphs that can have directed as well undirected edges are called mixed graphs, but such graphs are encountered rarely.

Graphs can be undirected or directed. In undirected graphs, the order of the endvertices of an edge is immaterial. An undirected edge joining vertices 
  
        u
        ,
        v
        ∈
        V
      
    {\displaystyle u, v \in V}
  
 is denoted by 
  
        {
        u
        ,
        v
        }
      
    {\displaystyle \{u, v\}}
  
. In directed graphs, each directed edge (arc) has an origin (tail) and a destination (head). An edge with origin 
  
        u
        ∈
        V
      
    {\displaystyle u \in V}
  
 and destination 
  
        v
        ∈
        V
      
    {\displaystyle v \in V}
  
 is represented by an ordered pair 
  
        (
        u
        ,
        v
        )
      
    {\displaystyle (u, v)}
  
. As a shorthand notation, an edge 
  
        {
        u
        ,
        v
        }
      
    {\displaystyle \{u, v\}}
  
 or 
  
        (
        u
        ,
        v
        )
      
    {\displaystyle (u, v)}
  
 can also be denoted by 
  
        u
        v
      
    {\displaystyle uv}
  
. In a directed graph, 
  
        u
        v
      
    {\displaystyle uv}
  
 is short for 
  
        (
        u
        ,
        v
        )
      
    {\displaystyle (u, v)}
  
, while in an undirected graph, 
  
        u
        v
      
    {\displaystyle uv}
  
 and 
  
        v
        u
      
    {\displaystyle vu}
  
 are the same and both stand for 
  
        {
        u
        ,
        v
        }
      
    {\displaystyle \{u, v\}}
  
. [...]. Graphs that can have directed edges as well as undirected edges are called mixed graphs, but such graphs are encountered rarely [...]

Anmerkungen

The source is not mentioned anywhere in the thesis.

The definitions given here are certainly standard and don't need to be quoted. However, Nm uses for several passages the same wording as the source.

Note also that "An edge with origin $u \in V$ is represented by an order pair $(u, v)$ " is a curious abbreviation of the statement "An edge with origin $u \in V$ and destination $v \in V$ is represented by an ordered pair $(u, v)$ " in the source.

Sichter: (Hindemith). WiseWoman

[2.] Nm/Fragment 099 26 - Diskussion
Zuletzt bearbeitet: 2012-04-24 23:07:40 WiseWoman

Brandes Erlebach 2005, Fragment, Gesichtet, KomplettPlagiat, Nm, SMWFragment, Schutzlevel sysop

Typus: KomplettPlagiat

Bearbeiter: Hindemith

Gesichtet

Untersuchte Arbeit:
Seite: 99, Zeilen: 26-32

Quelle: Brandes_Erlebach_2005
Seite(n): 8, Zeilen: 8-14

In both undirected and directed graphs', we may allow the edge set E to contain the same edge several times, that is, E can be a multiset. If an edge occurs several times in E, the copies of that edge are called parallel edges. Graphs with parallel edges are also called multigraphs. A graph is called simple, if each of its edges is contained in E only once, i.e., if the graph does not have parallel edges. An edge joining a vertex to itself, i.e., and edge whose end [vertices are identical, is called a loop.]

In both undirected and directed graphs, we may allow the edge set E to contain the same edge several times, i.e., E can be a multiset. If an edge occurs several times in E, the copies of that edge are called parallel edges. Graphs with parallel edges are also called multigraphs. A graph is called simple, if each of its edges is contained in E only once, i.e., if the graph does not have parallel edges. An edge joining a vertex to itself, i.e., an edge whose endvertices are identical, is called a loop.

Anmerkungen

The source is not given.

The definitions given here are certainly standard and don't need to be referenced. Nm, however, copied the formulation of those definitions word for word.

Sichter: (Hindemith), WiseWoman

[3.] Nm/Fragment 100 01 - Diskussion
Zuletzt bearbeitet: 2014-01-11 10:20:53 Hindemith

Brandes Erlebach 2005, Fragment, Gesichtet, Nm, SMWFragment, Schutzlevel sysop, Verschleierung

Typus: Verschleierung

Bearbeiter: Hindemith

Gesichtet

Untersuchte Arbeit:
Seite: 100, Zeilen: 1-16

Quelle: Brandes_Erlebach_2005
Seite(n): 8, 9, Zeilen: -

A graph is called loop-free if it has no loops.
A graph 
  
          G
          ′
        
        =
        (
        
          V
          ′
        
        ,
        
          E
          ′
        
        )
      
    {\displaystyle G' = (V' ,E')}
  
 is a subgraph of the graph 
  
        G
        =
        (
        V
        ,
        E
        )
      
    {\displaystyle G = (V, E)}
  
 if 
  
          V
          ′
        
        ⊆
        V
      
    {\displaystyle V' \subseteq V}
  
 and 
  
          E
          ′
        
        ⊆
        E
      
    {\displaystyle E' \subseteq E}
  
. It is a (vertex-)induced graph if 
  
          E
          ′
        
    {\displaystyle E'}
  
 contains all edges 
  
        e
        ∈
        E
      
    {\displaystyle e \in E}
  
 that join vertices in 
  
          V
          ′
        
    {\displaystyle V'}
  
.
Often it is useful to associate numerical values (weights) with the edges or vertices of a graph 
  
        G
        =
        (
        V
        ,
        E
        )
      
    {\displaystyle G = (V, E)}
  
. The graph having weights is known as weighted graph. Here we only discuss edge weights. Edge weights can be represented as a function 
  
        ω
        :
        E
        →
        
          R
        
    {\displaystyle \omega : E \to \mathbb{R}}
  
 that assigns each edge 
  
        e
        ∈
        E
      
    {\displaystyle e \in E}
  
, a weight 
  
        ω
        (
        e
        )
      
    {\displaystyle \omega(e)}
  
. Depending on the context, edge weights can describe various properties such as strength of interaction, or similarity. One usually tries to indicate the characteristics of the edge weights by the choice of the name of the function. For most purposes, an unweighted graph 
  
        G
        =
        (
        V
        ,
        E
        )
      
    {\displaystyle G = (V, E)}
  
 is equivalent to a weighted graph with unit edge weights 
  
        ω
        (
        e
        )
        =
        1
      
    {\displaystyle \omega(e) = 1}
  
 for all 
  
        e
        ∈
        E
      
    {\displaystyle e \in E}
  
.

[Page 8, line 14]
A graph is called loop-free if it has no loops.
[Page 9, line 4-6]
A graph 
  
          G
          ′
        
        =
        (
        
          V
          ′
        
        ,
        
          E
          ′
        
        )
      
    {\displaystyle G' = (V' ,E')}
  
 is a subgraph of the graph 
  
        G
        =
        (
        V
        ,
        E
        )
      
    {\displaystyle G = (V, E)}
  
 if 
  
          V
          ′
        
        ⊆
        V
      
    {\displaystyle V' \subseteq V}
  
 and 
  
          E
          ′
        
        ⊆
        E
      
    {\displaystyle E' \subseteq E}
  
. It is a (vertex-)induced subgraph if 
  
          E
          ′
        
    {\displaystyle E'}
  
 contains all edges 
  
        e
        ∈
        E
      
    {\displaystyle e \in E}
  
 that join vertices in 
  
          V
          ′
        
    {\displaystyle V'}
  
.
[Page 8, line 16ff]
Weighted graphs. Often it is useful to associate numerical values (weights) with the edges or vertices of a graph 
  
        G
        =
        (
        V
        ,
        E
        )
      
    {\displaystyle G = (V, E)}
  
. Here we discuss only edge weights. Edge weights can be represented as a function 
  
        ω
        :
        E
        →
        
          R
        
    {\displaystyle \omega : E \to \mathbb{R}}
  
 that assigns each edge 
  
        e
        ∈
        E
      
    {\displaystyle e \in E}
  
 a weight 
  
        ω
        (
        e
        )
      
    {\displaystyle \omega(e)}
  
.
Depending on the context, edge weights can describe various properties such as [...] strength of interaction, or similarity. One usually tries to indicate the characteristics of the edge weights by the choice of the name for the function. [...] For most purposes, an unweighted graph 
  
        G
        =
        (
        V
        ,
        E
        )
      
    {\displaystyle G = (V, E)}
  
 is equivalent to a weighted graph with unit edge weights 
  
        ω
        (
        e
        )
        =
        1
      
    {\displaystyle \omega(e) = 1}
  
 for all 
  
        e
        ∈
        E
      
    {\displaystyle e \in E}
  
.

Anmerkungen

The source is not given.

The definitions given here are certainly standard and don't need to be referenced. The author however copies not only the definitions but also their formulation word for word. The symbol for the real numbers used as the domain of the weight function is reproduced only as a box in the thesis, indicating that this character was not available in the font used.

Sichter: (Hindemith), WiseWoman