Complexity Analysis of Clique Problem

MAXIMUM CLIQUE PROBLEM the most relevant problem in Graph theory, known for years still do not have its polynomial time solution. Many algorithms have been proposed, still the problem lie the same i.e. to find the Clique in the polynomial time. The Clique problem is to figure out the sub graph with the maximum cardinality. Maximum clique in a random graph is NP-Hard problem, actuated by many prominent problems such as mobile networks, computer vision, & social network analysis. The paper is focused to serve an absolute review on Maximum Clique Problem. This paper encompass the survey done on the most studied algorithms of the Clique Problem with their results showing the best, average, and worst timing algorithms of Clique Problem. Though capturing the complete research in this regard is over the latitude of this paper, still it is tried to capture most of the ideal paper from similar approaches.