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Investigative Data Mining: Mathematical Models for Analyzing, Visualizing and Destabilizing Terrorist Networks

von Nasrullah Memon

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 Zuletzt bearbeitet: 2012-05-01 09:29:32 Hindemith Borgatti 2002, Fragment, Gesichtet, Nm, SMWFragment, Schutzlevel sysop, Verschleierung

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[The natural graphical representation of an adjacency matrix is a] table, such as shown in Figure 3. 2.

[TABLE, same as in source but extended by one row and one column]

Figure 3.2. Adjacency matrix for graph in Figure 3.1.

Examining either Figure 3.1 or Figure 3.2, we can see that not every vertex is adjacent to every other. A graph in which all vertices are adjacent to all others is said to be complete. The extent to which a graph is complete is indicated by its density, which is defined as the number of edges divided by the number possible. If self-loops are excluded, then the number possible is n(n-1)/2. Hence the density of the graph in Figure 3.1 is 7/21 = 0.33.

The natural graphical representation of an adjacency matrix is a table, such as

shown in Figure 2.

[TABLE]

Figure 2. Adjacency matrix for graph in Figure 1.

Examining either Figure 1 or Figure 2, we can see that not every vertex is adjacent to every other. A graph in which all vertices are adjacent to all others is said to be complete. The extent to which a graph is complete is indicated by its density, which is defined as the number of edges divided by the number possible. If self-loops are excluded, then the number possible is n(n-1)/2. [...] Hence the density of the graph in Figure 1 is 6/15 = 0.40.

 Anmerkungen The source is not given anywhere in the thesis. Sichter (Hindemith), Bummelchen

 Zuletzt bearbeitet: 2012-04-26 07:59:44 Fiesh Brandes Erlebach 2005, Fragment, Gesichtet, Nm, SMWFragment, Schutzlevel sysop, Verschleierung

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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

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