  A canonical problem in graph mining is the detection of dense communities.
This problem is exacerbated for a graph with a large order and size -- the
number of vertices and edges -- as many community detection algorithms scale
poorly. In this work we propose a novel framework for detecting active
communities that consist of the most active vertices in massive graphs. The
framework is applicable to graphs having billions of vertices and hundreds of
billions of edges. Our framework utilizes a parallelizable trimming algorithm
based on a locality statistic to filter out inactive vertices, and then
clusters the remaining active vertices via spectral decomposition on their
similarity matrix. We demonstrate the validity of our method with synthetic
Stochastic Block Model graphs, using Adjusted Rand Index as the performance
metric. We further demonstrate its practicality and efficiency on a most recent
real-world Hyperlink Web graph consisting of over 3.5 billion vertices and 128
billion edges.
