Algebraic Property Graphs (GQL Community Update, oct. 9, 2019)
•Download as PPTX, PDF•
0 likes•652 views
Algebraic Property Graphs is a formal data model for property graphs based on algebraic data types. It was developed for data integration at Uber and formalized at Conexus AI. APGs use type theory to allow for a schema and mapping language for property graphs. It also enables graph transformations, integration of non-graph datasets into graphs, and useful operations like queries, views, and conversions between graphs and algebraic databases.
![Algebraic Property Graphs
Joshua Shinavier (Uber), Ryan Wisnesky (Conexus AI)
[img]
GQL Community Update
October 9th, 2019](https://image.slidesharecdn.com/algebraicpropertygraphsgqlcommunityupdateoct-191009153739/85/Algebraic-Property-Graphs-GQL-Community-Update-oct-9-2019-1-320.jpg)
Recommended
More Related Content
What's hot
What's hot (20)
Similar to Algebraic Property Graphs (GQL Community Update, oct. 9, 2019)
Similar to Algebraic Property Graphs (GQL Community Update, oct. 9, 2019) (20)
More from Joshua Shinavier
More from Joshua Shinavier (13)
Recently uploaded
Recently uploaded (20)
Algebraic Property Graphs (GQL Community Update, oct. 9, 2019)
- 1. Algebraic Property Graphs Joshua Shinavier (Uber), Ryan Wisnesky (Conexus AI) [img] GQL Community Update October 9th, 2019
- 2. A formal data model for enterprise Property Graphs ● Things we need ○ Formal schema & mapping language for property graphs ○ Framework for graph transformation and integration ○ Means to build virtual graphs out of non-graph datasets (and vice versa) ● Algebraic Property Graphs ○ Based on algebraic data types ○ Developed for data integration at Uber ○ Formalized at Conexus AI ○ Strong connections to type theory, database theory, and category theory: ■ A familiar approach to type inference ■ Easy to reason about: all operations and proofs mechanically verified in Coq ■ Generalizes to algebraic databases
- 3. Product and sum types, Identifiers and values ● APG: ● Thrift example:
- 4. Algebraic types in common data interchange languages
- 5. Graph, schema, and data
- 6. Natural Transformations of Graphs, Schemas, and Data ● Non-natural transformations are also useful and are described in our paper.
- 7. Taxonomy of graph elements ● Vertex: “no data”. ● Edge: ordered pair of elements. ● Property: ordered pair (element, value). ○ Vertex property: element is a vertex. ○ Edge property: element is an edge ○ Meta-property: element is another property ■ Vertex / edge metaproperty, etc. ● Alias: contains another element ○ Vertex or edge “tags” ○ Aliases for primitive data types ● Hyperelement: everything else
- 8. Useful operations on Graphs, schemas, and data ● Conjunctive and disjunctive queries (select/from/where/union) ○ In: APGs and a predicate. Out: APG ● Views ○ In: APG and APG schema mapping. Out: ‘virtual’ APG ● Convert APGs to algebraic databases, and vice versa ○ In: Schema mapping and APG / algebraic database. Out: algebraic database / APG.
Editor's Notes
- Continuing with the TinkerPop 4 theme, I am going tell you about APG, or algebraic property graphs. This has been a collaboration between Uber and Conexus AI; tt the end of this slide show, there is a link to our paper.
- APG fills a need for a formal schema language for Property Graphs, and a formal approach to mappings. At Uber, we use it for developing company-wide standard schemas, and transforming schemas between the various schema languages we use. I had a presentation on an early version of APG last January at the Global Graph Summit, where I motivated formalizing property graph schemas in terms of category theory. Ryan, from Conexus AI, brought the mathematical expertise to make that happen. As a result, APG has strong connections to type theory and database theory, it is something that theorem provers can work with, and so on.
- The basic motivation was this. At Uber, and from what I know, also at other major tech companies like Google, LinkedIn, and so on, the vast majority of data is either relational or conforms to some system of algebraic data types. Here is an example of a struct, or product type, and an enum, or simple sum type, in Thrift. APG data types are simply algebraic data types that also include labels, in the sense of a vertex or edge label. The instance of a data type is a data value; on the top are the grammars that define legal types and values in APG.
- Here are the major data interchange languages use at Uber. GraphQL not so much; we included it for comparison, but we are very heavy on Thrift, Avro, and Protobuf, all of which have similar, informal type systems.
- This diagram captures the essence of APG. An algebraic property graph -- capital G -- consists of a set of elements, such as vertices and edges, a set of element labels, a set of data values, and a set of data types. I mentioned types and values on the last slide; they are made up of primitive types and values, element labels and element references, and sums and products. Each of the arrows between the four sets is a function -- for example, the lambda function takes you from an element like an edge to the label of that edge. The sigma function takes you from a label to the schema of that label. For example, the type of an edge label is a product of two vertex labels -- the label of the out-vertex and the label of the in-vertex. What is really important is that this diagram commutes; the schema of a label of an element is always the same as the type of the value of an element, which is the APG way of expressing the conformance of a graph to a graph schema.
- Just briefly, one of the really important objectives for APG was a formal notion of mappings between graphs, and we have that. The formalism supports varying degrees of naturality or preservation of semantics. This diagram shows the most natural, that is the most strict kind, a natural transformation.
- In TinkerPop3, there is an API called Graph.Features which allows you to specify, what kind of elements are supported in a graph, among other things. In APG, there are simple but formal definitions for what we call a vertex, an edge, a property, and so on, and it is easy to go beyond the typical property graph element classes if you need to. Meta-properties, meta-edges, and so on are just different classes of labels in terms of their schemas. At the bottom, you see some examples. A vertex is an element whose value is trivial; it has no internal structure. The value of an edge is an ordered pair of vertices. The value of a property is an ordered pair of an element and a primitive value.
- Last slide. One of the advantages of RDF over property graphs, historically, is that you can perform well-defined operations over them. Merging graphs, filtering graphs, and so on. In APG, these kinds of operations are also well-defined for property graphs. (More details if we have extra time)