  Applications in various domains rely on processing graph streams, e.g.,
communication logs of a cloud-troubleshooting system, road-network traffic
updates, and interactions on a social network. A labeled-graph stream refers to
a sequence of streamed edges that form a labeled graph. Label-aware
applications need to filter the graph stream before performing a graph
operation. Due to the large volume and high velocity of these streams, it is
often more practical to incrementally build a lossy-compressed version of the
graph, and use this lossy version to approximately evaluate graph queries.
Challenges arise when the queries are unknown in advance but are associated
with filtering predicates based on edge labels. Surprisingly common, and
especially challenging, are labeled-graph streams that have highly skewed label
distributions that might also vary over time. This paper introduces
Self-Balanced Graph Sketch (SBG-Sketch, for short), a graphical sketch for
summarizing and querying labeled-graph streams that can cope with all these
challenges. SBG-Sketch maintains synopsis for both the edge attributes (e.g.,
edge weight) as well as the topology of the streamed graph. SBG-Sketch allows
efficient processing of graph-traversal queries, e.g., reachability queries.
Experimental results over a variety of real graph streams show SBG-Sketch to
reduce the estimation errors of state-of-the-art methods by up to 99%.
