Finding cliques in graphs is a classical problem which is in general NP-hard and parameterized intractable. In typical applications like social networks or biological networks, however, the considered graphs are scale-free, i.e., their degree sequence follows a power law. Their specific structure can be algorithmically exploited and makes it possible to solve clique much more efficiently. We prove that on inhomogeneous random graphs with n nodes and power law exponent β, cliques of size k can be found in time O(n) for β≥3 and in time O(ne<sup>k4</sup>) for 2<β<3.
Friedrich, T., & Krohmer, A. (2015). Parameterized clique on inhomogeneous random graphs. Discrete Applied Mathematics, 184, 130–138. https://doi.org/10.1016/j.dam.2014.10.018