0422- A Little Graph Theory for Developers

7/27/2019 0422- A Little Graph Theory for Developers

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ALi%leGraphTheoryforthe

BusyDeveloper

Dr.JimWebber

ChiefScien@st,NeoTechnologyjimwebber


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Roadmap

Imprisoneddata Graphmodels Graphtheory

Localproper@es,globalbehavioursPredic@vetechniques

GraphmatchingPredic@ve,real-@meanaly@csforfunandprofit

Fin


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h%p://www.flickr.com/photos/crazyneighborlady/355232758/


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h%p://gallery.nen.gov.uk/image82582-.html


7/62h%p://www.xtranormal.com/watch/6995033/mongo-db-is-web-scale


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Aggregate-OrientedDatah%p://[email protected]/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)


11/62h%p://www.bbc.co.uk/london/travel/downloads/tube_map.html


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Propertygraphs

Propertygraphmodel:Nodeswithproper@esNamed,directedrela@onshipswithproper@esRela@onshipshaveexactlyonestartandendnode

Whichmaybethesamenode


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PropertyGraphModel


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PropertyGraphModel

TRAVELS_WITH

TRAVELS_W

ITH

LOVES


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PropertyGraphModel

TRAVELS_WITH

TRAVELS_W

ITH

LOVES

name: the Doctorage: 907

species: Time Lord

first name: Roselate name: Tyler

vehicle: tardismodel: Type 40


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LabeledPropertyGraphModel(Neo4j2.0)

TRAVELS_WITH

TRAVELS_W

ITH

LOVES

name: the Doctorage: 907

species: Time Lord

first name: Roselate name: Tyler

vehicle: tardismodel: Type 40

Label:human

Label:timelord


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Propertygraphsareverywhiteboard-friendly


18/62h%p://blogs.adobe.com/digitalmarke@ng/analy@cs/predic@ve-analy@cs/predic@ve-analy@cs-and-the-digital-marketer/


19/62h%p://en.wikipedia.org/wiki/File:Leonhard_Euler_2.jpg

MeetLeonhardEuler

Swissmathema@cian InventorofGraphTheory(1736)


20/62h%p://en.wikipedia.org/wiki/Seven_Bridges_of_Knigsberg


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TriadicClosure

name: Kyle

name: Stan name: Kenny


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TriadicClosure

name: Kyle


name: Kyle

name: Stan name: KennyFRIEND


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StructuralBalance

name: Cartman

name: Craig name: Tweek


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StructuralBalance

name: Cartman


name: Cartman

name: Craig name: TweekFRIEND


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StructuralBalance

name: Cartman


name: Cartman

name: Craig name: TweekENEMY


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StructuralBalance

name: Kyle


name: Kyle

name: Stan name: KennyFRIEND


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StructuralBalanceisakey

predic@vetechnique

Anditsdomain-agnos@c


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AlliesandEnemies

UK

GermanyFrance

Russia Italy

Austria


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AlliesandEnemies

UK

GermanyFrance

Russia Italy

Austria


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AlliesandEnemies

UK

GermanyFrance

Russia Italy

Austria


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AlliesandEnemies

UK

GermanyFrance

Russia Italy

Austria


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AlliesandEnemies

UK

GermanyFrance

Russia Italy

Austria


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AlliesandEnemies

UK

GermanyFrance

Russia Italy

Austria


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Predic@ngWWI[EasleyandKleinberg]


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StrongTriadicClosure

Itifanodehasstrongrela3onshipstotwo

neighbours,thentheseneighboursmusthaveat

leastaweakrela3onshipbetweenthem.

[Wikipedia]


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TriadicClosure(weakrela@onship)

name: Kenny

name: Stan name: Cartman


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TriadicClosure(weakrela@onship)

name: Kenny

name: Stan name: Cartman

name: Kenny

name: Stan name: CartmanFRIEND 50%


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Weakrela@onships

Rela@onshipscanhavestrengthaswellasintent

Think:weigh@ngonarela@onshipinapropertygraph

Weaklinksplayanothersuper-importantstructuralroleingraphtheory

Theybridgeneighbourhoods


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LocalBridges

FRIEND

name: Kenny

name: Stanname: KyleFRIENDFR

IEND

FRIEND

name: Sally

name: Bebename: WendyFRIENDF

RIEND

FRIEND 50%

name: CartmanFRIEND

ENEMY


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LocalBridgeProperty

IfanodeAinanetworksa3sfiestheStrong

TriadicClosurePropertyandisinvolvedinat

leasttwostrongrela3onships,thenanylocal

bridgeitisinvolvedinmustbeaweakrela3onship.

[EasleyandKleinberg]


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UniversityKarateClub


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GraphPar@@oning

(NP)HardproblemRecursivelyremovethespanninglinksbetweendenseregions

Orrecursivelymergenodesintoeverlargersubgraphnodes

Chooseyouralgorithmcarefullysomearebe%erthanothersforagivendomain

Canuseto(almostexactly)predictthebreakupofthekarateclub!


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UniversityKarateClubs(predictedbyGraphTheory)

9


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UniversityKarateClubs(whatactuallyhappened!)


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Cypher

Declara@vegraphpa%ernmatchinglanguageSQLforgraphsColumnarresults

Supportsgraphmatchingcommandsandqueries

FindmestufflikethisAggrega@on,orderingandlimit,etc.


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Firstname:MickeySurname: Smith

DoB: 19781006

SKU: 5e175641Product:Badgers

Nadgers Ale

SKU: 2555f258Product:Peewee Pilsner

Category: beer

SKU: 49d102bcProduct: BabyDry Nights

Category:nappies

Category: baby Category:alcoholicdrinks

SKU: 49d102bcProduct: XBox360

Category:consumerelectronics

Category:console

BOUGHTBOUGHT

MEMBER_

OF

MEMBER_OFMEMBER_OF

MEMBER_OFMEMBER_OF


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Firstname: *Surname: *DoB: 1996 > x

> 1972

Category: beerCategory:nappies

BOUGHTCategory: gameconsole


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Firstname: *Surname: *DoB: 1996 > x

> 1972

Category: beerCategory:nappies

!BOUGHTCategory: gameconsole


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(beer)(nappies)

(console)

(daddy)

()()


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Fla%enthegraph

(daddy)-[:BOUGHT]->()-[:MEMBER_OF]->(nappies)

(daddy)-[:BOUGHT]->()-[:MEMBER_OF]->(beer)

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


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WrapinaCypherMATCHclause

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

(daddy)-[:BOUGHT]->()-[:MEMBER_OF]->(beer),



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CypherWHEREclause

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

(daddy)-[:BOUGHT]->()-[:MEMBER_OF]->(beer),


WHERE b is null


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FullCypherquery

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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Whataregraphsgoodfor?

Recommenda@ons Businessintelligence Socialcompu@ng Geospa@al MDM Datacentremanagement Webofthings Genealogy Timeseriesdata Productcatalogue

Webanaly@cs Scien@ficcompu@ng(especiallybioinforma@cs) IndexingyourslowRDBMS Andmuchmore!

Co


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FreeOReillyeBook!

Visit:

h%p://GraphDatabases.com

Ian Robinson,Jim Webber & Emil Eifrem

Graph

Databases

h

Complim

ents

ofNeoTechnology


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ThanksforlisteningNeo4j:h"p://neo4j.org

Me:@jimwebber

Documents

0422- A Little Graph Theory for Developers