  Given a graph G and the desired size k in bits, how can we summarize G within
k bits, while minimizing the information loss?
  Large-scale graphs have become omnipresent, posing considerable computational
challenges. Analyzing such large graphs can be fast and easy if they are
compressed sufficiently to fit in main memory or even cache. Graph
summarization, which yields a coarse-grained summary graph with merged nodes,
stands out with several advantages among graph compression techniques. Thus, a
number of algorithms have been developed for obtaining a concise summary graph
with little information loss or equivalently small reconstruction error.
However, the existing methods focus solely on reducing the number of nodes, and
they often yield dense summary graphs, failing to achieve better compression
rates. Moreover, due to their limited scalability, they can be applied only to
moderate-size graphs.
  In this work, we propose SSumM, a scalable and effective graph-summarization
algorithm that yields a sparse summary graph. SSumM not only merges nodes
together but also sparsifies the summary graph, and the two strategies are
carefully balanced based on the minimum description length principle. Compared
with state-of-the-art competitors, SSumM is (a) Concise: yields up to 11.2X
smaller summary graphs with similar reconstruction error, (b) Accurate:
achieves up to 4.2X smaller reconstruction error with similarly concise
outputs, and (c) Scalable: summarizes 26X larger graphs while exhibiting linear
scalability. We validate these advantages through extensive experiments on 10
real-world graphs.
