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# Algebraic Property Graphs

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Slides about contents of the paper of Joshua Shinavier and Ryan Wisnesky. Presented by Adrian Wilke at the DICE (Data Science Group) colloquium.

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### Algebraic Property Graphs

1. 1. Algebraic Property Graphs Joshua Shinavier Ryan Wisnesky https://arxiv.org/pdf/1909.04881.pdf DICE colloquium presentation Adrian Wilke 2019-10-25 https://dice-research.org/
2. 2. Authors 2 Joshua Shinavier Uber Technologies One of the three co-founders of TinkerPop [JS] image: https://on.mktw.net/2MbIZTW Ryan Wisnesky Conexus AI “[...] algebraic property graphs as a simple but mathematically rigorous bridge between graph and non-graph data models [...]” B.S. and M.S. degrees in mathematics and computer science from Stanford University and a Ph.D. in computer science from Harvard University, where he studied the design and implementation of provably correct software systems. Previously, he was a postdoctoral associate in the MIT department of mathematics, where he developed the categorical query language, CQL. He currently leads open-source and commercial development of CQL as CTO of Conexus AI. https://www.wisnesky.net APG listed as case study for Categorical Query Language (CQL) at categoricaldata.net/papers
3. 3. Contents 3 15 text pages 7.6 pages appendix 2.3 pages toc & ref
4. 4. Contents 4 “main contribution” motivation short introduction
5. 5. Motivation: Property graphs ⇄ RDF 5 slide source: [CDL]
6. 6. Motivation: Property graphs ⇄ RDF 6 slide source: [CDL]
7. 7. Motivation: Property graphs 7 also: missing semantics in several implementations slide source: [CDL]
8. 8. Motivation: Hypergraphs 8 slide source: [CDL]
9. 9. Category theory 9
10. 10. Category theory 10 “In mathematics, abstract nonsense [...] are terms used by mathematicians to describe abstract methods related to category theory.” https://en.wikipedia.org/w/index.php?title=Abstract_nonsense&oldid=881291659
11. 11. Category theory 11
12. 12. Category theory: Morphisms and composition 12
13. 13. example 2 source: [EC] Category theory: Morphisms and composition 13
14. 14. Category theory: Functors 14
15. 15. Algebraic Property Graphs Deﬁnition 15
16. 16. AGP: - P - t ∈ P primitive types - V(t) primitive values - four sets - four functions - equation 16 AGP: deﬁnition
17. 17. 17 AGP: deﬁnition labels: think of classes in OOP
18. 18. 18 AGP: deﬁnition t1 ⨉ t2 e.g. for edges edge(nodeA, nodeB) think of types in OOP
19. 19. 19 AGP: deﬁnition value used for vertex labels elements: think of objects in OOP
20. 20. AGP: deﬁnition 20 elements: think of objects in OOP
21. 21. AGP: deﬁnition 21 labels: think of classes in OOP lambda like label elements: think of objects in OOP
22. 22. AGP: deﬁnition 22 sigma 🠖 schema tau 🠖 type G(𝓣): types of G G(𝓣): types of G
23. 23. AGP: deﬁnition 23
24. 24. AGP: deﬁnition 24 Composition g ○ f g( f(x) ) Image: https://en.wikipedia.org/wiki/Morphism
25. 25. Taxonomy & examples 25
26. 26. Taxonomy: Vertices 26
27. 27. Taxonomy: Vertices 27
28. 28. Taxonomy: Edges 28 t1 ⨉ t2 e.g. for edges edge(nodeA, nodeB) We already saw this.
29. 29. Taxonomy: Edges 29
30. 30. Taxonomy: Properties 30
31. 31. Taxonomy: Properties 31
32. 32. Migrating AGPs 32
33. 33. Migrating AGPs 33 obviously not.
34. 34. RDF ⇄ AGP 34 free category is the category that results from freely concatenating arrows together, whenever the target of one arrow is the source of the next.
35. 35. RDF ⇄ AGP 35
36. 36. Summary 36 “We propose algebraic property graphs as a simple but mathematically rigorous bridge between graph and non-graph data models.”
37. 37. Summary 37 “main contribution” motivation short introduction
38. 38. For further research 38 ● Java implementation https://github.com/CategoricalData/CQL/tree/master/src/main/java/catdata/apg ● Coq proofs (paper footnote 9) https://www.categoricaldata.net/APG.v ● [CDL] Joshua Shinavier: In Search of the Universal Data Model (Connected Data London 2019) https://youtu.be/telyBQCuq70 ● Joshua Shinavier: Algebraic Property Graphs (GQL Community Update) https://www.slideshare.net/joshsh/algebraic-property-graphs-gql-community-update-oct-9-2019 ● Research on CQL https://www.categoricaldata.net/papers Related to RDF: “Formal Modelling and Application of Graph Transformations in the Resource Description Framework” (doctoral dissertation) ● [JS] Joshua Shinavier: Position statement for the W3C Workshop on Graph Data, 2019 https://www.w3.org/Data/events/data-ws-2019/assets/position/Joshua%20Shinavier.pdf ● [EC] Category Theory in Life - Eugenia Cheng https://youtu.be/ho7oagHeqNc