Complex networks: Structure and dynamics

TLDR: The major concepts and results recently achieved in the study of the structure and dynamics of complex networks are reviewed, and the relevant applications of these ideas in many different disciplines are summarized, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.

About: This article is published in Physics Reports.The article was published on 2006-02-01 and is currently open access. It has received 9441 citations till now. The article focuses on the topics: Network dynamics & Complex network.

Figures

Fig. 5.4. Reprinted figure with permission from Ref. [450]. 2005 by the American Physical Society. (a) N/ 2 (in logarithmic scale) for random graphs vs. . (b) c (see text for definition) vs. the parameter space ( ,B). Random networks have 〈k〉 = 2m = 4, identical to that of scale free networks. In the domain where c < 0 scale free networks synchronize better than random networks. Same conditions as in the caption of Fig. 5.3.

Fig. 6.8. (a) In- and out-degree distributions averaged over a set of 43 different organisms. (b) The diameter of the metabolic network as a function of the number N of metabolites in the E. Coli. (c) The average number of outgoing edges vs. the number of nodes.

Fig. 2.1. Graphical representation of a undirected (a), a directed (b), and a weighted undirected (c) graph with N = 7 nodes and K = 14 links. In the directed graph, adjacent nodes are connected by arrows, indicating the direction of each link. In the weighted graph, the values wi,j reported on each link indicate the weights of the links, and are graphically represented by the link thicknesses.

Fig. 2.3. Communities can be defined as groups of nodes such that there is a higher density of edges within groups than between them. In the case shown in figure there are three communities, denoted by the dashed circles. Reprinted figure with permission from Ref. [51]. 2004 by the American Physical Society.

Fig. 2.13. Color coded maps representing the spatial distributions of centrality in Cairo, an example of a largely self-organized city. The four indices of node centrality, (a) closeness; (b) betweenness; (c) straightness and (d) information, are visually compared over the spatial graph. Different colors represent classes of nodes with different values of the centrality index. The classes are defined in terms of multiples of standard deviations from the average, as reported in the color legend. Figure taken from Ref. [47].

Fig. 3.5. Total number of active packets as a function of time steps in the model by Echenique et al. [336] with steady input of packets. Panels (a) and (b) correspond to the standard protocol, while (c) and (d) have been obtained for the traffic-aware routing with h = 0.85. In each panel, the continuous line stands for subcritical values of p ((a) and (b) p = 3.0, (d) p = 8.0) and the dotted line corresponds to p>pc ((a) and (b) p = 4.0, (c) and (d) p = 13.0). Reprinted figure with permission from Ref. [336]. 2005 by the European Physical Society.

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The authors review the major concepts and results recently achieved in the study of the structure and dynamics of complex networks, and summarize the relevant applications of these ideas in many different disciplines, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.