Embodiments of the present invention provide a system for fast parallel graph compression based on identifying a set of large cliques, which is used to encode the graph. The system provides both permanently-stored and in-memory graph encoding and reduces the space needed to represent and store a graph, the I/O traffic to use the graph, and the computation needed to perform algorithms involving the graph. The system thereby improves computing technology and graph computation. During operation, the system obtains data indicating vertices and edges of a graph. The system executes a clique-finding method to identify a maximum clique in the graph. The system then removes the clique from the graph, adds the clique to a set of found cliques, and generates a compressed representation of the graph based on the set of found cliques.