Incremental and Parallel Computation of Structural Graph Summaries for Evolving Graphs

Graph summarization is the task of finding condensed representations of graphs such that a chosen set of (structural) subgraph features in the graph summary are equivalent to the input graph. Existing graph summarization algorithms are tailored to specific graph summary models, only support one-time batch computation, are designed and implemented for a specific task, or evaluated using static graphs. Our novel, incremental, parallel algorithm addresses all these shortcomings. We support various structural graph summary models defined in our formal language FLUID. All graph summaries defined with FLUID can be updated in time O(Δ · dk), where Δ is the number of additions, deletions, and modifications to the input graph, d is its maximum degree, and k is the maximum distance in the subgraphs considered. We empirically evaluate the performance of our algorithm on benchmark and real-world datasets. Our experiments show that, for commonly used summary models and datasets, the incremental summarization algorithm almost always outperforms their batch counterpart, even when about $50%$ of the graph database changes. The source code and the experimental results are openly available for reproducibility and extensibility.