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

Abstract

Summarization is a widespread method to handle very large graphs. The task of structural graph summarization is to compute a concise while at the same time meaningful synopsis of the key structural information of the graph. As there are many tasks regarding what information is to be summarized from a graph, there is no single concept or model of graph summaries. We have studied existing structural graph summaries for large (semantic) graphs. Despite the different purposes and concepts followed by the existing graph summaries, we found common patterns in the captured graph structures. We abstract from these patterns and provide for the first time a formally defined common model FLUID (FLexible graph sUmmarIes for Data graphs) that allows to flexibly define structural graph summaries. FLUID allows to quickly define, adapt, and compare different graph summaries for different purposes and datasets. To this end, FLUID provides features of structural summarization based on equivalence relations such as distinction of types and properties, direction of edges, bisimulation, and inference. We conduct a detailed complexity analysis of the features provided by FLUID. We show that graph summaries defined with FLUID can be computed in the worst case in $\\mathcal{O}(n^2)$ w.r.t. $n$ the number of edges in the data graph. However, we analyzed large-scale graphs obtained from the web with billions of edges and found indications that the average complexity is bounded by $\\Theta(n)$. Finally, we provide a formal declarative language for FLUID, which allows application developers to quickly define and modify their graph summaries. The language can be used to build any of the existing structural graph summaries found in the literature and beyond. In addition, FLUID can be extended by new summarization features by defining further equivalence relations over graph structures.