Busy Developer Dr. Jim Webber Chief Scientist, Neo Technology - - PowerPoint PPT Presentation

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busy developer

Busy Developer Dr. Jim Webber Chief Scientist, Neo Technology - - PowerPoint PPT Presentation

Aug 22, 2023 476 likes •1.23k views

A Little Graph Theory for the Busy Developer Dr. Jim Webber Chief Scientist, Neo Technology @jimwebber Roadmap Imprisoned data Graph models Graph theory Local properties, global behaviours Predictive techniques Graph

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A Little Graph Theory for the Busy Developer

Dr. Jim Webber

Chief Scientist, Neo Technology @jimwebber

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Roadmap

Imprisoned data
Graph models
Graph theory

– Local properties, global behaviours – Predictive techniques

Graph matching

– Predictive, real-time analytics for fun and profit

Fin

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http://www.flickr.com/photos/crazyneighborlady/355232758/

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http://gallery.nen.gov.uk/image82582-.html

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http://www.xtranormal.com/watch/6995033/mongo-db-is-web-scale

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Aggregate-Oriented Data

http://martinfowler.com/bliki/AggregateOrientedDatabase.html

“There is a significant downside - the whole approach works really well when data access is aligned with the aggregates, but what if you want to look at the data in a different way? Order entry naturally stores orders as aggregates, but analyzing product sales cuts across the aggregate structure. The advantage of not using an aggregate structure in the database is that it allows you to slice and dice your data different ways for different audiences. This is why aggregate-oriented stores talk so much about map-reduce.”

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complexity = f(size, connectedness, uniformity)

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http://www.bbc.co.uk/london/travel/downloads/tube_map.html

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Property graphs

Property graph model:

– Nodes with properties – Named, directed relationships with properties – Relationships have exactly one start and end node

Which may be the same node

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Property Graph Model

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Property Graph Model

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Property Graph Model

name: the Doctor age: 907 species: Time Lord first name: Rose late name: Tyler vehicle: tardis model: Type 40

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Labeled Property Graph Model

(Neo4j 2.0)

name: the Doctor age: 907 species: Time Lord first name: Rose late name: Tyler vehicle: tardis model: Type 40 Label:human Label:timelord

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Property graphs are very whiteboard-friendly

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http://blogs.adobe.com/digitalmarketing/analytics/predictive-analytics/predictive-analytics-and-the-digital-marketer/

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http://en.wikipedia.org/wiki/File:Leonhard_Euler_2.jpg

Meet Leonhard Euler

Swiss mathematician
Inventor of Graph

Theory (1736)

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http://en.wikipedia.org/wiki/Seven_Bridges_of_Königsberg

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Triadic Closure

name: Kyle name: Stan name: Kenny

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Triadic Closure

name: Kyle name: Stan name: Kenny name: Kyle name: Stan name: Kenny

FRIEND

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Structural Balance

name: Cartman name: Craig name: Tweek

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Structural Balance

name: Cartman name: Craig name: Tweek name: Cartman name: Craig name: Tweek

FRIEND

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Structural Balance

name: Cartman name: Craig name: Tweek name: Cartman name: Craig name: Tweek

ENEMY

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Structural Balance

name: Kyle name: Stan name: Kenny name: Kyle name: Stan name: Kenny

FRIEND

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Structural Balance is a key predictive technique

And it’s domain-agnostic

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Allies and Enemies

UK Germany France Russia Italy Austria

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Allies and Enemies

UK Germany France Russia Italy Austria

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Allies and Enemies

UK Germany France Russia Italy Austria

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Allies and Enemies

UK Germany France Russia Italy Austria

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Allies and Enemies

UK Germany France Russia Italy Austria

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Allies and Enemies

UK Germany France Russia Italy Austria

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Predicting WWI

[Easley and Kleinberg]

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Strong Triadic Closure

It if a node has strong relationships to two neighbours, then these neighbours must have at least a weak relationship between them. [Wikipedia]

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Triadic Closure

(weak relationship)

name: Kenny name: Stan name: Cartman

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Triadic Closure

(weak relationship)

name: Kenny name: Stan name: Cartman name: Kenny name: Stan name: Cartman

FRIEND 50%

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Weak relationships

Relationships can have “strength” as well as

intent

– Think: weighting on a relationship in a property graph

Weak links play another super-important

structural role in graph theory

– They bridge neighbourhoods

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Local Bridges

FRIEND

name: Kenny name: Stan name: Kyle

FRIEND FRIEND

name: Sally name: Bebe name: Wendy

FRIEND FRIEND 50%

name: Cartman

FRIEND ENEMY

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Local Bridge Property

“If a node A in a network satisfies the Strong Triadic Closure Property and is involved in at least two strong relationships, then any local bridge it is involved in must be a weak relationship.” [Easley and Kleinberg]

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University Karate Club

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Graph Partitioning

(NP) Hard problem

– Recursively remove the spanning links between dense regions – Or recursively merge nodes into ever larger “subgraph” nodes – Choose your algorithm carefully – some are better than others for a given domain

Can use to (almost exactly) predict the

break up of the karate club!

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University Karate Clubs

(predicted by Graph Theory)

9

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University Karate Clubs

(what actually happened!)

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Cypher

Declarative graph pattern matching language

– “SQL for graphs” – Columnar results

Supports graph matching queries

– And aggregation, ordering and limit, etc. – Mutation

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Cypher is Declarative

Imperative

– follow relationship – breadth-first vs depth- first – explicit algorithm

Declarative

– specify starting point – specify desired outcome – algorithm adaptable – based on query

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Cypher is a pattern matching language

A C B

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Un-named Nodes & Rels

() --> ()

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Un-named Relationship

(A) --> (B)

B A

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ASCII Art Patterns

A -[:LOVES]-> B

LOVES

B A

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ASCII Art Patterns

A --> B --> C

C B A

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ASCII Art Patterns

A --> B --> C, A --> C A --> B --> C <-- A

A C B

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Variable Length Paths

A -[*]-> B

A B A B A B

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Optional Relationships

A -[?]-> B

A B

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Example Query

The top 5 most frequently appearing

companions:

start doctor=node:characters(character = 'Doctor') match (doctor)<-[:COMPANION_OF]-(companion)

[:APPEARED_IN]->(episode)

return companion.character, count(episode)

rder by count(episode) desc

limit 5 Start node from index Subgraph pattern Accumulates rows by episode Limit returned rows

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Firstname: Mickey Surname: Smith DoB: 19781006 SKU: 5e175641 Product: Badgers Nadgers Ale SKU: 2555f258 Product: Peewee Pilsner Category: beer SKU: 49d102bc Product: Baby Dry Nights Category: nappies Category: baby Category: alcoholic drinks SKU: 49d102bc Product: XBox 360 Category: consumer electronics Category: console

BOUGHT BOUGHT MEMBER_OF MEMBER_OF MEMBER_OF MEMBER_OF MEMBER_OF

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Firstname: * Surname: * DoB: 1996 > x > 1972 Category: beer Category: nappies

BOUGHT

Category: game console

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Firstname: * Surname: * DoB: 1996 > x > 1972 Category: beer Category: nappies

!BOUGHT

Category: game console

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(beer) (nappies) (console) (daddy) () () ()

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Flatten the graph

(daddy)-[:BOUGHT]->()-[:MEMBER_OF]->(nappies) (daddy)-[:BOUGHT]->()-[:MEMBER_OF]->(beer) (daddy)-[b:BOUGHT]->()-[:MEMBER_OF]->(console)

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Wrap in a Cypher MATCH clause

MATCH (daddy)-[:BOUGHT]->()-[:MEMBER_OF]->(nappies), (daddy)-[:BOUGHT]->()-[:MEMBER_OF]->(beer), (daddy)-[b:BOUGHT]->()-[:MEMBER_OF]->(console)

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Cypher WHERE clause

MATCH (daddy)-[:BOUGHT]->()-[:MEMBER_OF]->(nappies), (daddy)-[:BOUGHT]->()-[:MEMBER_OF]->(beer), (daddy)-[b:BOUGHT]->()-[:MEMBER_OF]->(console) WHERE b is null

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Full Cypher query

START beer=node:categories(category=‘beer’), nappies=de:categories(category=‘nappies’), xbox=node:products(product=‘xbox 360’) MATCH (daddy)-[:BOUGHT]->()-[:MEMBER_OF]->(beer), (daddy)-[:BOUGHT]->()-[:MEMBER_OF]->(nappies), (daddy)-[b?:BOUGHT]->(xbox) WHERE b is null RETURN distinct daddy

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Results

==> +---------------------------------------------+ ==> | daddy | ==> +---------------------------------------------+ ==> | Node[15]{name:"Rory Williams",dob:19880121} | ==> +---------------------------------------------+ ==> 1 row ==> 6 ms ==> neo4j-sh (0)$

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What are graphs good for?

Recommendations
Business intelligence
Social computing
Geospatial
MDM
Systems management
Web of things
Genealogy
Time series data
Product catalogue
Web analytics
Scientific computing (especially bioinformatics)
Indexing your slow RDBMS
And much more!

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Free O’Reilly eBook!

Visit: http://GraphDatabases.com

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Thanks for listening

Neo4j: http://neo4j.org Neo Technology: http://neotechnology.com Me: @jimwebber

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Neo4j Meetup in Hilversum Next Week