  Complex networks has been a hot topic of research over the past several years
over crossing many disciplines, starting from mathematics and computer science
and ending by the social and biological sciences. Random graphs were studied to
observe the qualitative features they have in common in planetary scale data
sets which helps us to project the insights proven to real world networks.
  In this paper, We survey the particular case of small-world phenomena and
decentralized search algorithms. We start by explaining the first empirical
study for the six degrees of separation phenomenon in social networks; then we
review some of the probabilistic network models based on this work, elaborating
how these models tried to explain the phenomenon properties, and lastly, we
review few of the recent empirical studies empowered by these models. Finally,
some future works are proposed in this area of research.
