Incremental and Parallel Computation of Structural Graph Summaries for Evolving Graphs

Abstract

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(∆ •d k), where ∆ 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.

FLUID: A common model for semantic structural graph summaries based on equivalence relations

“…Goasdoué et al [18] justify this assumption, via their hypothesis ( ), and provide an alternative data structure using Tarjan's algorithm instead of hash maps. In a previous work, we found evidence that supports their hypothesis, i. e., that the numbers of incoming and outgoing predicates for each vertex are, in practice, bounded [5].…”

“…The vertex summary vs y is a subgraph in SG that is equivalent to the subgraphs of all summarized vertices v ∈ [y] EQR in G under EQR. For vertex summaries, we distinguish primary vertices, which are equivalence classes of EQR, and secondary vertices, which are equivalence classes of the relations from which EQR is defined [5]. Furthermore, we can attach payload [19] to each primary vertex in a vertex summary vs ⊆ SG.…”

Scaling R-GCN Training with Graph Summarization

“…These are referred to as forward, backward and forward/backward [17] bisimulation. In this paper, we use the FLUID framework [4], which allows us to create a forward (k)-bisimulation summary. Figure 3a represents a small fragment of a KG.…”

“…To compute the Attribute Summary, we use a SPARQL query developed by Campinas [7] and a slightly modified version which also gives us the mappings. To compute the forward (k)-bisimulation, we use the FLUID framework [4,5]. We then also generate the mapping from the summary nodes to the original nodes.…”