1. A Graph is a Graph is a Graph:
Equivalence, Transformations, and
Composition of Graph Data Models
Joshua Shinavier, PhD
Global Graph Summit 2019
26.01.2019

2. • Graphs
• Categories
• Data models
• Transformations
• Graphs @ Uber
Outline

3. Graphs

15. TinkerFactory.createClassic() + vertex labels

16. Graph structure

17. Categories

19. An object

20. An arrow (morphism)

22. Composition

23. Identity

25. An isomorphism

26. An isomorphism: f-1
∘f = ida
, f∘f-1
= idb

27. An isomorphism

29. Composition of isomorphisms

30. A category

32. A functor

33. Equivalence

34. Graphs and operations as a category

36. Equivalent models

37. Data models

38. • Property Graphs
• Resource Description Framework (RDF)
• Relational Model
• SQL, CQL, HQL, DQL, ...
• Data interchange formats
• Protocol Buffers, Apache Thrift, Apache Avro
• Mostly based on algebraic data types (ADTs)
Some data models of interest (@ Uber)

39. • A simple interpretation1
I of an RDF graph is:
• A non-empty set IR of resources, called the domain or universe of I
• A set IP, called the set of properties of I
• A mapping IEXT from IP into 𝒫(IR x IR), i.e. the set of sets of pairs <x, y> with
x and y in IR
• Assuming:
• Ground RDF graphs only (⇒ no blank nodes)
Resource Description Framework (RDF)
1) World Wide Web Consortium. (2014). RDF 1.1 concepts and abstract syntax.

40. • Simple.
• Vertices, edges, properties
• No standard
• W3C Property Graphs working group (2013)
• W3C Graph Data Workshop (March 2019)
• Next best thing?
• TinkerPop’s Graph.Features
Property Graph data model

41. • Many are concerned with the data model
• Vertex/edge id data types
• Numeric, string, UUID, “any”
• Property support
• Supports vertex properties? edge properties? vertex metaproperties?
• Multi-properties?
• Property data types
• Primitive: boolean, byte, double, float, integer, long, string
• Complex: array, map, list (uniform/mixed), serializable
TinkerPop’s Graph.Features

42. Property graph objects
v = a vertex label (e.g. Person, Place, Dataset)
e = an edge label (e.g. knows, likes, claims)
p = a property key (e.g. name, weight)
d = a data type (e.g. String, Integer, List<String>)

43. Edges

44. Vertex properties

45. Edge properties

46. Vertex meta-properties

47. Meta-edges: edge to vertex

48. Meta-edge: vertex to edge

49. Bonus: hyper-edge

50. Bonus: RDF statement

51. Transformations

52. • neo4j-rdf-sail (2008-2010)
• Wrapper based on OpenRDF (now RDF4J) Sail API
• Neo4j-internal representation of RDF resources and statements
• Blueprints RDF suite (2010-2014)
• SailGraph: pragmatic RDF → PG mapping
• GraphSail: storage and retrieval of RDF data in a PG database
• PropertyGraphSail: PG → RDF mappings (simple vs. lossless)
• Cudré-Mauroux et al. 2013: RDF storage and query on various NoSQL backends
• Hartig 2014: formal PG ↔ RDF* mappings (simple vs. lossless and invertible)
• Das et al. 2014: PG → RDF mappings (reification-, NG-, subproperty-based)
• SPARQL-Gremlin (2015-present): SPARQL → Gremlin query mapping
• jbarrasa/neosemantics (2016-present): RDF storage/query on Neo4j
• etc.
Example: Property Graphs ↔ RDF

53. • We want them:
• Bidirectional
• Composable
• Techniques
• Bidirectional arrows
• Symmetric lenses
• Symmetric currying
Graph transformations

57. Goal: define an isomorphism

58. Problem: internal structure is not one-to-one

59. ...but some components are analogous

60. Asymmetric context

61. Symmetric context
Fruit images: Wikipedia, PicsArt, PNG Mart, PNG Only, toppng

62. Graphs @ Uber

63. • Let’s build a knowledge graph
• E.g. Riders, drivers, trips, vehicles, orders, etc.
• Evaluate OLTP and OLAP queries
• Use cases:
• Risk and safety, recommendation, analytics
Goal

64. • Thousands of datasets and schemas
• Static, streaming, RPC
• Data sources are not composable
• Strong identifiers, weak semantics
• Duplicate types, homonyms, synonyms
• Per-language data islands
• Diversity of data modeling conventions
Problems

65. • Define mappings on a per-dataset basis
• Great precision, low recall
• Build bridges between data models
• Must be composable
• Standardized vocabulary saves a lot of pain
• Commonly-used types and properties
• E.g. basic data types, time, geometry and geolocation, addresses
and contact info, sensors, money, etc.
• Shared logical data model
• Tooling for transformations
• Written in Haskell, compiles to bytecode via Eta
Solutions
UBER KNOWLEDGE GRAPH

66. Building bridges

67. Logical

68. YAML

69. Protocol Buffers

70. Apache Thrift

71. Apache Avro

72. N-Triples (OWL)

73. Docs

74. Thanks
joshsh@uber.com