  We propose a fast, parallel maximum clique algorithm for large sparse graphs
that is designed to exploit characteristics of social and information networks.
The method exhibits a roughly linear runtime scaling over real-world networks
ranging from 1000 to 100 million nodes. In a test on a social network with 1.8
billion edges, the algorithm finds the largest clique in about 20 minutes. Our
method employs a branch and bound strategy with novel and aggressive pruning
techniques. For instance, we use the core number of a vertex in combination
with a good heuristic clique finder to efficiently remove the vast majority of
the search space. In addition, we parallelize the exploration of the search
tree. During the search, processes immediately communicate changes to upper and
lower bounds on the size of maximum clique, which occasionally results in a
super-linear speedup because vertices with large search spaces can be pruned by
other processes. We apply the algorithm to two problems: to compute temporal
strong components and to compress graphs.
