## FANDOM

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 Bearbeitet: 11. January 2014, 23:32 (WiseWoman)Erstellt: 10. January 2014, 22:54 Hindemith

Untersuchte Arbeit:
Seite: 435, Zeilen: 9-17
Quelle: Brandes Erlebach 2005
Seite(n): 7, 8, Zeilen: 7: 30ff; 8: 1ff
Graphs can be undirected or directed. The adjacency matrix of an undirected graph 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 ordered pair $(u, v)$. As a shorthand notation, an edge $\{u, v\}$ can also be denoted by $uv$. It should be noted that, 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 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 paper. But note that the content here are the very basics of graph theory and found at many places (however not always in the same wording). After the title of chapter there is a footnote 2, which reads: 2 Most of the concepts discussed in this section are taken from [22]. (22. West, B.D.: Introduction to Graph Theory, 2nd edn. Prentice Hall, Englewood Cliffs (2001)) Sichter (Hindemith), WiseWoman

 Bearbeitet: 11. January 2014, 23:33 (Hindemith)Erstellt: 11. January 2014, 14:22 Hindemith

Consider a network representing a symmetrical relation, “communicates with” for a set of nodes. When a pair of nodes (say, u and v) is linked by an edge so that they can communicate directly without intermediaries, they are said to be adjacent. A set of edges linking two or more modes [sic] (u, v, w) such that node u would like to communicate with w, using node v. Consider a graph representing the symmetrical relation, "communicates with" for a set of people. When a pair of points is linked by an edge so that they can communicate directly without intermediaries, they are said to be adjacent. A set of edges linking two or more points $(p_i, p_j, p_k)$ such that $p_i$ is adjacent to $p_j$ and $p_j$ is adjacent to $p_k$ constitute a path from $p_i$ to $p_k$.