Stability notions in synthetic graph generation: a preliminary study

With the rise in adoption of massive graph data, it be- comes increasingly important to design graph processing algorithms which have predictable behavior as the graph scales. This work presents an initial study of stability in the context of a schema-driven synthetic graph generation. Specifically, we study the design of algorithms which gener- ate high-quality sequences of graph instances. Some desir- able features of these sequences include monotonic contain- ment of graph instances as they grow in size and consistency of structural properties across the sequence. Such stabil- ity features are important in understanding and explaining the scalability of many graph algorithms which have cross- instance dependencies (e.g., solutions for role detection in dynamic networks and graph query processing). We imple- ment a preliminary approach in the recently proposed open- source synthetic graph generator gMark and demonstrate its viability in generating stable sequences of graphs.