Compact Structure for Sparse Undirected Graphs based on a Clique Graph Partition

Felipe Glaria, Cecilia Hernandez, Susana Ladra, Gonzalo Navarro, and Lilian Salinas

Compressing real-world graphs has many benefits such as improving or enabling the visualization in small memory devices, graph query processing, community search, and mining algorithms. This work proposes a novel compact representation for real sparse and clustered undirected graphs. The approach lists all the maximal cliques by using a fast algorithm and defines a clique graph based on its maximal cliques. Further, the method defines a fast and effective heuristic for finding a clique graph partition that avoids the construction of the clique graph. Finally, this partition is used to define a compact representation of the input graph. The experimental evaluation shows that this approach is competitive with the state-of-the-art methods in terms of compression efficiency and access times for neighbor queries, and that it recovers all the maximal cliques faster than using the original graph. Moreover, the approach makes it possible to query maximal cliques, which is useful for community detection.