Random hyperbolic graphs
By Marcos Kiwi
Also appears in collection : IX Latin and American algorithms, graphs and optimization symposium (LAGOS 2017) / 9e symposium latino et americain des algorithmes, graphes et de l'optimisation (LAGOS 2017)
Random hyperbolic graphs (RHG) were proposed rather recently (2010) as a model of real-world networks. Informally speaking, they are like random geometric graphs where the underlying metric space has negative curvature (i.e., is hyperbolic). In contrast to other models of complex networks, RHG simultaneously and naturally exhibit characteristics such as sparseness, small diameter, non-negligible clustering coefficient and power law degree distribution. We will give a slow pace introduction to RHG, explain why they have attracted a fair amount of attention and then survey most of what is known about this promising infant model of real-world networks.
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