# Nm/Fragment 111 17

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 Typus KomplettPlagiat Bearbeiter Graf Isolan Gesichtet
Untersuchte Arbeit:
Seite: 111, Zeilen: 17-27
Quelle: Holmgren 2006
Seite(n): 956, Zeilen: right column 18-32
In graph theory a number of measures have been proposed to characterize networks. However, three concepts are particularly important in contemporary studies of the topology of complex networks: degree distribution, clustering coefficient, and average path length (Albert, R., and Barabasi, A.L. (2002); Dorogovtsev, S. N., and Mendes, J. F. F. (2002); Newman, M. E. J. (2003)).

3.4.1 Degree Distribution

The degree $k_i$ is the number of edges connecting to the i$^{th}$ vertex. The vertex degree is characterized by a distribution function P(k), which gives the probability that a randomly selected vertex has k edges. Recent studies show that several complex networks have a [heterogeneous topology, i.e., some vertices have a very large number of edges, but the majority of the vertices only have a few edges.]

In graph theory, a number of measures have been proposed to characterize networks. However, three concepts are particularly important in contemporary studies of the topology of complex networks: degree distribution, clustering coefficient, and average path length. [EN 1-3]

2.2.1. Degree Distribution

The degree $k_i$ is the number of edges connecting to vertex i. The vertex degree is characterized by a distribution function P(k), which gives the probability that a randomly selected vertex has k edges. Recent studies show that several complex networks have a heterogeneous topology, i.e., some vertices have a very large number of edges, but the majority of the vertices only have a few edges.

[EN 1]. Albert, R., & Barabási, A.-L. (2002). Statistical mechanics of complex networks. Reviews of Modern Physics, 74, 47–97.

[EN 2]. Dorogovtsev, S. N., & Mendes, J. F. F. (2002). Evolution of networks. Advances in Physics, 51, 1079–1187.

[EN 3]. Newman, M. E. J. (2003). The structure and function of complex networks. SIAM Review, 45, 167–256.

 Anmerkungen Nearly identical, though the source is not mentioned anzwhere. Sichter (Graf Isolan), Hindemith