# Nm/113

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

von Nasrullah Memon

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[The] so-called small-world property appears to characterize many complex networks. Despite their often-large size, there is a relatively short path between any two vertices in a network: the average shortest paths between a pair of vertices scales as the logarithm of the number of vertices.

3.5 GRAPHS AS MODELS OF REAL-WORLD NETWORKS

The study of networks, and in particular the interest in the statistical measures of the topology of networks (see section 3.4), has given birth to three main classes of network models. The random graph was introduced by Erdos and Renyi in the late 1950s and is one of the earliest theoretical models of a network (Bollobas, B., 1985). This is the easiest model to analyze mathematically and it can serve as a reference for randomness. Watts and Strogatz introduced the so called small world model in 1998 (Watts, D. J., and Strogatz, S. H., 1998). This model combines high clustering and a short average path length.

In 1999, Barabasi and Albert (BA) addressed the origin of the power-law degree distribution, evident in many real networks, with a simple model (also known as the scale-free network model) that put the emphasis on how real networks evolve (Albert, R., Jeong, H., and Barabasi, A.L., 2000).

The so-called small-world property appears to characterize many complex networks. Despite their often-large size, there is a relatively short path between any two vertices in the network: the average shortest paths between

a pair of vertices scales as the logarithm of the number of vertices.

2.3. Graphs as Models of Real-World Networks

2.3.1. Theoretical Network Models

The study of networks, and in particular the interest in the statistical measures of the topology of networks (previous section), has given birth to three main classes of network models. The random graph was introduced by Erdös and Rènyi in the late 1950s and is one of the earliest theoretical models of a network. [EN 12] This is the easiest model to analyze mathematically and it can serve as a reference for randomness. Watts and Strogatz introduced the so-called small world model in 1998. [EN 4] This model combines high clustering and a short average path length. In 1999, Barabási and Albert (BA) addressed the origin of the power-law degree distribution, evident in many real networks, with a simple model (also known as the scale-free network model) that put the emphasis on how real networks evolve. [EN 13]

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[EN 4]. Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of “small-world” networks. Nature, 393, 440–442.

[EN 12]. Bollobás, B. (1985). Random Graphs. London: Academic Press.

[EN 13]. Albert, R., Jeong, H., & Barabási, A.-L. (2000). Error and attack tolerance of complex networks. Nature, 406, 378–382.

 Anmerkungen The third page of text which is identical to Holmgren (2006). No source given. Sichter (Graf Isolan), Hindemith

 Zuletzt bearbeitet: 2012-04-21 15:23:21 Hindemith Chen 2006, Fragment, Gesichtet, Nm, SMWFragment, Schutzlevel sysop, Verschleierung

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Three models have been used to distinguish complex networks: random graph model, small-world model, and scale-free model (Albert and Barabasi, 2002). It is to note that most complex systems are not random but are governed by some well known principles encoded in the topology of the networks. Three models have been employed to characterize complex networks: random graph model, small-world model, and scale-free model (Albert & Barabasi, 2002). Most complex systems are not random but are governed by certain organizing principles encoded in the topology of the networks.
 Anmerkungen Nm writes sentences that can also be found in a book of one of Nm's referees. Moreover, in view of what Nm has written in the previous paragraphs the first sentence with its reference does not make much sense, since it is more or less a repetition of a list given further above. Sichter (Graf Isolan), Hindemith

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