## FANDOM

33.175 Seiten

 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 $G' = (V' ,E')$ is a subgraph of the graph $G = (V, E)$ if $V' \subseteq V$ and $E' \subseteq E$. It is a (vertex-)induced graph if $E'$ contains all edges $e \in E$ that join vertices in $V'$.

Often it is useful to associate numerical values (weights) with the edges or vertices of a graph $G = (V, E)$. The graph having weights is known as weighted graph. Here we only discuss edge weights. Edge weights can be represented as a function $\omega : E \to \mathbb{R}$ that assigns each edge $e \in E$, a weight $\omega(e)$. 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 $G = (V, E)$ is equivalent to a weighted graph with unit edge weights $\omega(e) = 1$ for all $e \in E$.

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A graph is called loop-free if it has no loops.

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A graph $G' = (V' ,E')$ is a subgraph of the graph $G = (V, E)$ if $V' \subseteq V$ and $E' \subseteq E$. It is a (vertex-)induced subgraph if $E'$ contains all edges $e \in E$ that join vertices in $V'$.

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Weighted graphs. Often it is useful to associate numerical values (weights) with the edges or vertices of a graph $G = (V, E)$. Here we discuss only edge weights. Edge weights can be represented as a function $\omega : E \to \mathbb{R}$ that assigns each edge $e \in E$ a weight $\omega(e)$.

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 $G = (V, E)$ is equivalent to a weighted graph with unit edge weights $\omega(e) = 1$ for all $e \in E$.

 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