  Summarizing graphs w.r.t. structural features is important to reduce the
graph's size and make tasks like indexing, querying, and visualization
feasible. Our generic parallel BRS algorithm efficiently summarizes large
graphs w.r.t. a custom equivalence relation $\sim$ defined on the graph's
vertices $V$. Moreover, the definition of $\sim$ can be chained $k\geq 1$
times, so the defined equivalence relation becomes a $k$-bisimulation. We
evaluate the runtime and memory performance of the BRS algorithm for
$k$-bisimulation with $k=1,\ldots,10$ against two algorithms found in the
literature (a sequential algorithm due to Kaushik et al. and a parallel
algorithm of Sch\"atzle et al.), which we implemented in the same software
stack as BRS. We use five real-world and synthetic graph datasets containing
100 million to two billion edges. Our results show that the generic BRS
algorithm outperforms the respective native bisimulation algorithms on all
datasets for all $k\geq5$ and for smaller $k$ in some cases. The BRS
implementations of the two bisimulation algorithms run almost as fast as each
other. Thus, the BRS algorithm is an effective parallelization of the
sequential Kaushik et al. bisimulation algorithm.
