Finding maximum clique in a distance matrix created by certain pattern
Although the question lacks some details, I propose my solution to the general version of your problem.

Yes. It really depends on the "pattern" based on which you create the graph. There is an infinite number of patterns. For example, one can propose a simple pattern that makes it easy to find the cliques in linear time:

Pattern 1: There is a link between two vertices if the labels of the vertices are two consecutive numbers.
Clique detection algorithm? Simply list the cliques "{1,2}, {2,3}, ..., {n-1, n}".

Pattern 2: There is a link between two vertices if their distance in the original graph is at most two.
Clique detection algorithm? Np-hard problem.