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Exploring complex networks

Abstract

The study of networks pervades all of science, from neurobiology to statistical physics. The most basic issues are structural: how does one characterize the wiring diagram of a food web or the Internet or the metabolic network of the bacterium Escherichia coli? Are there any unifying principles underlying their topology? From the perspective of nonlinear dynamics, we would also like to understand how an enormous network of interacting dynamical systems — be they neurons, power stations or lasers — will behave collectively, given their individual dynamics and coupling architecture. Researchers are only now beginning to unravel the structure and dynamics of complex networks.

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Figure 1: Wiring diagrams for complex networks.
Figure 2: Spontaneous synchronization in a network of limit-cycle oscillators with distributed natural frequencies.
Figure 3: Schematic illustration of regular and random network architectures.
Figure 4: Solvable model of a small-world network.
Figure 5: Average path length, normalized by system size, is plotted as a function of the average number of shortcuts.
Figure 6: Degree distributions for real networks.
Figure 7: Bipartite versus unipartite representations of the corporate director network.
Figure 8: Structural properties of the Fortune 1,000 network of corporate directors for 1999.

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Acknowledgements

Thanks to J. Ariaratnam, A.-L. Barabasi, N. Martinez, M. E. J. Newman, D. Watts and A. Winfree for their comments on a draft of the manuscript, and to R. Albert, L. Amaral, M. Amin, W. Blake, A. Broder, D. Callaway, J. Collins, G. Davis, H. Ebel, K. Kohn, N. Martinez, R. Oliva, M. E. J. Newman, J. Thorp, D. Watts, J. Wiener, A. Winfree and H. Wang for providing data, figures and information. Research supported in part by the National Science Foundation, Department of Defense, and Electric Power Research Institute.

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Strogatz, S. Exploring complex networks. Nature 410, 268–276 (2001). https://doi.org/10.1038/35065725

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