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We developed a flexible parallel algorithm for graph summarization based onvertex-centric programming and parameterized message passing. The basealgorithm supports infinitely many structural graph summary models defined in aformal language. An extension of the parallel base algorithm allows incrementalgraph summarization. In this paper, we prove that the incremental algorithm iscorrect and show that updates are performed in time $\mathcal{O}(\Delta \cdotd^k)$, where $\Delta$ is the number of additions, deletions, and modificationsto the input graph, $d$ the maximum degree, and $k$ is the maximum distance inthe subgraphs considered. Although the iterative algorithm supports values of$k>1$, it requires nested data structures for the message passing that arememory-inefficient. Thus, we extended the base summarization algorithm by ahash-based messaging mechanism to support a scalable iterative computation ofgraph summarizations based on $k$-bisimulation for arbitrary $k$. Weempirically evaluate the performance of our algorithms using benchmark andreal-world datasets. The incremental algorithm almost always outperforms thebatch computation. We observe in our experiments that the incremental algorithmis faster even in cases when $50\%$ of the graph database changes from oneversion to the next. The incremental computation requires a three-layered hashindex, which has a low memory overhead of only $8\%$ ($\pm 1\%$). Finally, theincremental summarization algorithm outperforms the batch algorithm even withfewer cores. The iterative parallel $k$-bisimulation algorithm computessummaries on graphs with over $10$M edges within seconds. We show that thealgorithm processes graphs of $100+\,$M edges within a few minutes while havinga moderate memory consumption of $<150$ GB. For the largest BSBM1B dataset with1 billion edges, it computes $k=10$ bisimulation in under an hour.

Time and Memory Efficient Parallel Algorithm for Structural Graph  Summaries and two Extensions to Incremental Summarization and  $k$-Bisimulation for Long $k$-Chaining