FANDOM

33.178 Seiten

 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 $u, v \in V$ is denoted by $\{u, v\}$.

In directed graphs, each directed edge (arc) has an origin (tail) and a destination (head). An edge with origin $u \in V$ is represented by an order pair $(u, v)$. As a shorthand notation, an edge $\{u, v\}$ can also be denoted by $uv$. It is to note that, in a directed graph, $uv$ is short for $(u, v)$, while in an undirected graph, $uv$ and $vu$ are the same and both stands for $\{u, v\}$. 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 $u, v \in V$ is denoted by $\{u, v\}$. In directed graphs, each directed edge (arc) has an origin (tail) and a destination (head). An edge with origin $u \in V$ and destination $v \in V$ is represented by an ordered pair $(u, v)$. As a shorthand notation, an edge $\{u, v\}$ or $(u, v)$ can also be denoted by $uv$. In a directed graph, $uv$ is short for $(u, v)$, while in an undirected graph, $uv$ and $vu$ are the same and both stand for $\{u, v\}$. [...]. 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