  Given a labeled graph, the frequent-subgraph mining (FSM) problem asks to
find all the $k$-vertex subgraphs that appear with frequency greater than a
given threshold. FSM has numerous applications ranging from biology to network
science, as it provides a compact summary of the characteristics of the graph.
However, the task is challenging, even more so for evolving graphs due to the
streaming nature of the input and the exponential time complexity of the
problem.
  In this paper, we initiate the study of the approximate FSM problem in both
incremental and fully-dynamic streaming settings, where arbitrary edges can be
added or removed from the graph. For each streaming setting, we propose
algorithms that can extract a high-quality approximation of the frequent
$k$-vertex subgraphs for a given threshold, at any given time instance, with
high probability. In contrast to the existing state-of-the-art solutions that
require iterating over the entire set of subgraphs for any update, our
algorithms operate by maintaining a uniform sample of $k$-vertex subgraphs with
optimized neighborhood-exploration procedures local to the updates. We provide
theoretical analysis of the proposed algorithms and empirically demonstrate
that the proposed algorithms generate high-quality results compared to
baselines.
