Formalizing Gremlin pattern matching traversals in an integrated graph Algebra

Graph data management (also called NoSQL) has revealed beneficial characteristics in terms of flexibility and scalability by differ-ently balancing between query expressivity and schema flexibility. This peculiar advantage has resulted into an unforeseen race of developing new task-specific graph systems, query languages and data models, such as property graphs, key-value, wide column, resource description framework (RDF), etc. Present-day graph query languages are focused towards flex-ible graph pattern matching (aka sub-graph matching), whereas graph computing frameworks aim towards providing fast parallel (distributed) execution of instructions. The consequence of this rapid growth in the variety of graph-based data management systems has resulted in a lack of standardization. Gremlin, a graph traversal language, and machine provide a common platform for supporting any graph computing sys-tem (such as an OLTP graph database or OLAP graph processors). In this extended report, we present a formalization of graph pattern match-ing for Gremlin queries. We also study, discuss and consolidate various existing graph algebra operators into an integrated graph algebra