A Little Graph Theory for the Busy Developer

A
Li%le
Graph
Theory
for
the

Busy
Developer

Jim
Webber

Chief
Scien?st,
Neo
Technology

@jimwebber

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Watch the video with slide
synchronization on InfoQ.com!
http://www.infoq.com/presentations
/graph-database-theory

Presented at QCon New York
www.qconnewyork.com
Purpose of QCon
- to empower software development by facilitating the spread of
knowledge and innovation
Strategy
- practitioner-driven conference designed for YOU: influencers of
change and innovation in your teams
- speakers and topics driving the evolution and innovation
- connecting and catalyzing the influencers and innovators
Highlights
- attended by more than 12,000 delegates since 2007
- held in 9 cities worldwide

Roadmap

•  Imprisoned
data

•  Graph
models

•  Graph
theory

– Local
proper?es,
global
behaviors

– Predic?ve
techniques

•  Graph
matching

– Real-‐?me
analy?cs
for
fun
and
proﬁt

•  Fin

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

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

Aggregate-‐Oriented
Data

h%p://mar?nfowler.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.”

complexity = f(size, connectedness, uniformity)

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

Property
graphs

•  Property
graph
model:

– Nodes
with
proper?es

– Named,
directed
rela?onships
with
proper?es

– Rela?onships
have
exactly
one
start
and
end
node

•  Which
may
be
the
same
node

stole

from

loves

loves

enemy

enemy

A
Good
Man

Goes
to
War

appeared

in

appeared

in

appeared

in

appeared

in

Victory
of

the
Daleks

appeared

in

appeared

in

companion

companion

enemy

Property
graphs
are
very
whiteboard-‐friendly

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

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

Meet
Leonhard
Euler

•  Swiss
mathema?cian

•  Inventor
of
Graph

Theory
(1736)

16

Königsberg
(Prussia)
-‐
1736

A

B

D

C

1"
2"
3"
4"
7"
6"
5"

h%p://en.wikipedia.org/wiki/Seven_Bridges_of_Königsberg

20

Triadic
Closure

name: Kyle
name: Stan name: Kenny

Triadic
Closure

name: Kyle
name: Kyle
FRIEND

Structural
Balance

name: Cartman
name: Craig name: Tweek

Structural
Balance

name: Cartman
name: Cartman
FRIEND

Structural
Balance

name: Cartman
name: Cartman
ENEMY

Structural
Balance

name: Kyle
name: Kyle
FRIEND

Structural
Balance
is
a
key

predic?ve
technique

And
it’s
domain-‐agnos?c

Allies
and
Enemies

UK

Germany
France

Russia
Italy

Austria

Predic?ng
WWI

[Easley
and
Kleinberg]

Strong
Triadic
Closure

It
if
a
node
has
strong
rela3onships
to
two

neighbours,
then
these
neighbours
must
have
at

least
a
weak
rela3onship
between
them.

[Wikipedia]

Triadic
Closure

(weak
rela?onship)

name: Kenny
name: Stan name: Cartman

Triadic
Closure

(weak
rela?onship)

name: Kenny
name: Kenny
FRIEND 50%

Weak
rela?onships

•  Rela?onships
can
have
“strength”
as
well
as

intent

– Think:
weigh?ng
on
a
rela?onship
in
a
property

graph

•  Weak
links
play
another
super-‐important

structural
role
in
graph
theory

– They
bridge
neighbourhoods

Local
Bridges

FRIEND
name: Kenny
name: Stanname: Kyle
FRIENDFRIEND
FRIEND
name: Sally
name: Bebename: Wendy
FRIENDFRIEND
FRIEND 50%
name: Cartman
FRIEND
ENEMY

Local
Bridge
Property

“If
a
node
A
in
a
network
sa3sﬁes
the
Strong

Triadic
Closure
Property
and
is
involved
in
at

least
two
strong
rela3onships,
then
any
local

bridge
it
is
involved
in
must
be
a
weak

rela3onship.”

[Easley
and
Kleinberg]

University
Karate
Club

Graph
Par??oning

•  (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
be%er

than
others
for
a
given
domain

•  Can
use
to
(almost
exactly)
predict
the

break
up
of
the
karate
club!

University
Karate
Clubs

(predicted
by
Graph
Theory)

9

University
Karate
Clubs

(what
actually
happened!)

Cypher

•  Declara?ve
graph
pa%ern
matching
language

– “SQL
for
graphs”

– Columnar
results

•  Supports
graph
matching
commands
and

queries

– Find
me
stuﬀ
like
this…

– Aggrega?on,
ordering
and
limit,
etc.

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
BOUGHTBOUGHT
MEMBER_OF
MEMBER_OFMEMBER_OF
MEMBER_OFMEMBER_OF

Firstname: *
Surname: *
DoB: 1996 > x
> 1972
Category: beerCategory:
nappies
BOUGHTCategory: game
console

Firstname: *
Surname: *
DoB: 1996 > x
> 1972
Category: beerCategory:
nappies
!BOUGHTCategory: game
console

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

Fla%en
the
graph

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

Wrap
in
a
Cypher
MATCH
clause

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

Cypher
WHERE
clause

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

Full
Cypher
query

START beer=node:categories(category=‘beer’),
nappies=node: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

Results

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

Facebook
Graph
Search

Which
sushi
restaurants
in

NYC
do
my
friends
like?

Cypher
query

START me=node:person(name = 'Jim'),
location=node:location(location='New York'),
cuisine=node:cuisine(cuisine='Sushi')
MATCH (me)-[:IS_FRIEND_OF]->(friend)-[:LIKES]->(restaurant)
-[:LOCATED_IN]->(location),(restaurant)-[:SERVES]->(cuisine)
RETURN restaurant

What
are
graphs
good
for?

•  Recommenda?ons

•  Pharmacology

•  Business
intelligence

•  Social
compu?ng

•  Geospa?al

•  MDM

•  Data
center
management

•  Web
of
things

•  Genealogy

•  Time
series
data

•  Product
catalogue

•  Web
analy?cs

•  Scien?ﬁc
compu?ng

•  Indexing
your
slow
RDBMS

•  And
much
more!

Free
O’Reilly
book
for

everyone!

h%p://graphdatabases.com

Ian Robinson,
Jim Webber & Emil Eifrem
Graph
Databases
h Com
plim
ents
ofNeo
Technology

Thanks
for
listening

Neo4j:
h"p://neo4j.org

Me:
@jimwebber

Watch the video with slide synchronization on
InfoQ.com!
http://www.infoq.com/presentations/graph-
database-theory

A Little Graph Theory for the Busy Developer

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