Summary
In this chapter, after a short survey of recent developments in the theory of complex networks, we discuss a class of random graph models for complex networks where the exceptional and Xevents play a crucial role in the formation of network structures. Indeed, some vertices — the “hubs” — have an extremely high number of connections to other vertices, whereas most vertices have just a few. These networks are generally “scale-free”; in other words, they exhibit architectural and statistical stability as the degree distribution grows. We also relate some extremal properties of the diameters of random graphs to the thresholds of epidemic processes, and we discuss robustness against system damage.
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Blanchard, P., Krüger, T. (2006). Networks of the Extreme: A Search for the Exceptional. In: Albeverio, S., Jentsch, V., Kantz, H. (eds) Extreme Events in Nature and Society. The Frontiers Collection. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28611-X_12
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DOI: https://doi.org/10.1007/3-540-28611-X_12
Publisher Name: Springer, Berlin, Heidelberg
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