Nearest-neighbor directed random hyperbolic graphs

I. A. Kasyanov, P. van der Hoorn, D. Krioukov, and M. V. Tamm
Physical Review E
Kasyanov, I. A., van der Hoorn, P., Krioukov, D., & Tamm, M. V. (2023). Nearest-neighbour directed random hyperbolic graphs. Physical Review E 10.1103/PhysRevE.108.054310
November 21, 2023


Undirected hyperbolic graph models have been extensively used as models of scale-free small-world networks with high clustering coefficient. Here we presented a simple directed hyperbolic model where nodes randomly distributed on a hyperbolic disk are connected to a fixed number m of their nearest spatial neighbors. We introduce also a canonical version of this network (which we call “network with varied connection radius”), where maximal length of outgoing bond is space dependent and is determined by fixing the average out-degree to m. We study local bond length, in-degree, and reciprocity in these networks as a function of spacial coordinates of the nodes and show that the network has a distinct core-periphery structure. We show that for small densities of nodes the overall in-degree has a truncated power-law distribution. We demonstrate that reciprocity of the network can be regulated by adjusting an additional temperature-like parameter without changing other global properties of the network.

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