In this paper, we study the maximum clique problem on hyperbolic random graphs. A hyperbolic random graph is a mathematical model for analyzing scale-free networks since it effectively explains the power-law degree distribution of scale-free networks. We propose a simple algorithm for finding a maximum clique in hyperbolic random graph. We first analyze the running time of our algorithm theoretically. We can compute a maximum clique on a hyperbolic random graph G in O(m+n4.5(1−α)) expected time if a geometric representation is given or in O(m+n6(1−α))
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expected time if a geometric representation is not given, where
n
and
m
denote the numbers of vertices and edges of
G
, respectively, and
α
denotes a parameter controlling the power-law exponent of the degree distribution of
G
. Also, we implemented and evaluated our algorithm empirically. Our algorithm outperforms the previous algorithm [BFK18] practically and theoretically. Beyond the hyperbolic random graphs, we have experiment on real-world networks. For most of instances, we get large cliques close to the optimum solutions efficiently.