  There are many methods to find a maximum (or maximal) clique in large
networks. Due to the nature of combinatorics, computation becomes exponentially
expensive as the number of vertices in a graph increases. Thus, there is a need
for efficient algorithms to find a maximum clique. In this paper, we present a
graph reduction method that significantly reduces the order of a graph, and so
enables the identification of a maximum clique in graphs of large order, that
would otherwise be computational infeasible to find the maximum. We find bounds
of the maximum (or maximal) clique using this reduction. We demonstrate our
method on real-life social networks and also on Erd\"{o}s-Renyi random graphs.
