20150610 nick mccullen

EDEn Energy and the Design of Environments

Modelling the Spread ofEnergy Innovations in Cities

Nick McCullen

Research Centre for Energy and the Design of Environments (EDEn)Department of Architecture and Civil Engineering

University of Bath

LUCAS Seminar, Nottingham, 10th June 2015


Table of Contents

Cities and Energy Use

Complex Systems and Networks

Modelling the Diffusion of Energy Innovation

Using Real-World Data to Inform the Models

Comparing Intervention Scenarios

Cities and Energy

Future Energy Decision Making for Cities:Can Complexity Science Rise to the Challenge?

With: Catherine Bale, Timothy Foxon, William Gale, Alastair Rucklidge. (Leeds)

I Cities are expanding:I Over 50% people living in cities,I by 2050: 60%–80%

I Buildings consume 20%–40% of total energy.I Local authorities can influence residents/businesses to reduce

energy demand.I Decision-making tools are needed to support their potential

contribution to energy and climate change targets‡.

‡: Bale, et al. “Strategic energy planning within local authorities in the UK:

A study of the city of Leeds.” Energy Policy (2012)c©Jasvipul Chawla

1 / 33

Cities and Energy




I Buildings consume 20%–40% of total energy.

I Local authorities can influence residents/businesses to reduceenergy demand.

I Decision-making tools are needed to support their potentialcontribution to energy and climate change targets‡.



1 / 33

Cities and Energy




I Buildings consume 20%–40% of total energy.I Local authorities can influence residents/businesses to reduce

energy demand.I Decision-making tools are needed to support their potential

contribution to energy and climate change targets‡.



1 / 33


Cities and Energy

Understanding energy behaviour

2 / 33


Cities and Energy

Domestic energy use

I Energy use depends on both technology and behaviour:

I use of installed tech &decisions to install.

I Roll-out of energy efficiencytechnologies is a problem.

c©BRE

I can we create models of energy innovation uptake?

3 / 33


Cities and Energy

Why is energy different?

I Model of uptake of technology.I E.g. Smart-phones:

I visible and socially desirable,I mediated by social contacts between individuals.

I Energy technologies:I sometimes visible (solar panels).

I can be hidden (e.g. loft insulation),I decisions based on individual benefit.

http://www.greendayrenewables.com http://www.homeinsulationgrants.com

4 / 33


Cities and Energy




I Energy technologies:I sometimes visible (solar panels).

I can be hidden (e.g. loft insulation),I decisions based on individual benefit.

http://www.greendayrenewables.com

http://www.homeinsulationgrants.com

4 / 33


Cities and Energy




I Energy technologies:I sometimes visible (solar panels).I can be hidden (e.g. loft insulation),I decisions based on individual benefit.

http://www.greendayrenewables.com http://www.homeinsulationgrants.com

4 / 33



Complex systems

I System of many interacting components,

I interactions are important,

I dynamics governed by rules or equationsof interaction,

I behaviour of whole system emergesnaturally through interactions:

I “emergent properties”.

5 / 33

AAbbey Road F3Abbey Wood G4Acton Central B3Acton Main Line B3Acton Town B3Addington Village E6Addiscombe E6Albany Park G5Aldgate E3Aldgate East E3Alexandra Palace E1All Saints F3Alperton B2Amersham A1Ampere Way D5Anerley E5Angel E3Angel Road F1Archway D2Arena E5Arnos Grove E1Arsenal E2Avenue Road F5

BBaker Street C3Balham C5Bank E3Banstead C6Barbican D3Barking G3Barkingside G2Barnehurst H4Barnes C4Barnes Bridge B4Barons Court C3Battersea Park C4Bayswater C3Beckenham Hill F5Beckenham Junction F5Beckenham Road F5Beckton G4Beckton Park G3Becontree H2Beddington Lane D5Belgrave Walk C5Bellingham F5Belmont C6Belsize Park D2Belvedere G4Bermondsey E4Berrylands B5Bethnal Green (LU) E3Bethnal Green

(Greater Anglia) E3Bexley G5Bexleyheath G4Bickley G5Birkbeck E5Blackfriars D3Blackheath F4Blackhorse Lane E6Blackhorse Road F2Blackwall F3Bond Street C3Borough D4Boston Manor A3Bounds Green E1Bow Church F3Bowes Park E1Bow Road F3Brent Cross C2Brentford B4Brentwood H1Brimsdown F1Brixton D4Brockley E4Bromley-by-Bow F3Bromley North F5Bromley South F5Brondesbury C2Brondesbury Park C2Broxbourne F1Bruce Grove F2Buckhurst Hill G1Burnt Oak C1Bushey B1Bush Hill Park F1

CCaledonian Road E2Caledonian Road

& Barnsbury E2Cambridge Heath E2Camden Road D2Camden Town D2Canada Water E4Canary Wharf F4Canning Town F3Cannon Street E3Canonbury E2Canons Park C1Carpenders Park B1Carshalton D6Carshalton Beeches D6Castle Bar Park A3Caterham E6Catford F5Catford Bridge F5Centrale D6Chadwell Heath H2Chafford Hundred H2Chalfont & Latimer A1Chalk Farm D2Chancery Lane D3Charing Cross D3Charlton G4Cheam C6

C continuedChelsfield G5Chesham A1Cheshunt F1Chessington North B6Chessington South B6Chigwell G1Chingford F1Chipstead D6Chislehurst G5Chiswick B4Chiswick Park B3Chorleywood A1Church Street D6City Thameslink D3Clapham Common D4Clapham High Street D4Clapham Junction C4Clapham North D4Clapham South D4Clapton F2Clock House F5Cockfosters E1Colindale C1Colliers Wood C5Coombe Lane E6Coulsdon South D6Coulsdon Town D6Covent Garden D3Crayford H5Crews Hill E1Cricklewood C2Crofton Park F5Crossharbour F4Crouch Hill E2Croxley A1Crystal Palace E5Custom House for

ExCeL G3Cutty Sark for

Maritime Greenwich F4Cyprus G3

DDagenham Dock H3Dagenham East H2Dagenham Heathway H2Dalston Junction E2Dalston Kingsland E2Debden G1Denmark Hill D4Deptford F4Deptford Bridge F4Devons Road F3Dollis Hill C2Drayton Green A3Drayton Park E2Dundonald Road C5

EEaling Broadway B3Ealing Common B3Earl’s Court C3Earlsfield C4East Acton B3Eastcote B2East Croydon E6East Dulwich D4East Finchley D1East Ham G3East India F3East Putney C4Eden Park F5Edgware C1Edgware Road C3Edmonton Green F1Elephant & Castle D4Elmers End F5Elm Park H2Elmstead Woods G5Elstree &

Borehamwood C1Eltham G4Elverson Road F4Embankment D3Emerson Park H2Emirates Greenwich

Peninsula F4Emirates Royal Docks G3Enfield Chase E1Enfield Lock F1Enfield Town F1Epping G1Epsom Downs C6Erith H4Essex Road E3Euston D3Euston Square D3Ewell East C6Ewell West C6

FFairlop G2Falconwood G4Farringdon D3Feltham A5Fenchurch Street E3Fieldway F6Finchley Central D1Finchley Road C2Finchley Road & Frognal C2Finsbury Park E2Forest Gate G2Forest Hill E5Fulham Broadway C4Fulwell A5

GGallions Reach G3Gants Hill G2George Street E6Gidea Park H2

G continuedGipsy Hill D5Gloucester Road C3Golders Green D2Goldhawk Road B3Goodge Street D3Goodmayes G2Gordon Hill E1Gospel Oak D2Grange Hill G1Grange Park E1Gravel Hill E6Grays H3Great Portland Street D3Greenford A2Green Park C3Greenwich F4Grove Park F5Gunnersbury B4

HHackbridge D6Hackney Central F2Hackney Downs F2Hackney Wick F2Hadley Wood E1Haggerston E3Hainault G1Hammersmith B3Hampstead D2Hampstead Heath D2Hampton A5Hampton Court A5Hampton Wick B5Hanger Lane B3Hanwell A3Harlesden B2Harold Wood H2Harringay E2Harringay Green Lanes E2Harrington Road E5Harrow & Wealdstone B1Harrow-on-the-Hill B2Hatch End B1Hatton Cross A4Haydons Road C5Hayes E6Hayes & Harlington A3Headstone Lane B1Heathrow

Terminals 1, 2, 3 A4Heathrow Terminal 4 A4Heathrow Terminal 5 A4Hendon C2Hendon Central C2Herne Hill D5Heron Quays F4Highams Park F1High Barnet D1Highbury & Islington E2Highgate D2High Street Kensington C3Hillingdon A1Hither Green F5Holborn D3Holland Park C3Holloway Road E2Homerton F2Honor Oak Park E5Hornchurch H2Hornsey E2Hounslow A4Hounslow Central A4Hounslow East A4Hounslow West A4Hoxton E3Hyde Park Corner C3

IIckenham A1Ilford G2Imperial Wharf C4Island Gardens F4Isleworth A4

KKenley E6Kennington D4Kensal Green B2Kensal Rise C2Kensington (Olympia) C3Kent House E5Kentish Town D2Kentish Town West D2Kenton B1Kew Bridge B4Kew Gardens B4Kidbrooke F4Kilburn C2Kilburn High Road C2Kilburn Park C2King George V G4King Henry’s Drive F6King’s Cross D3Kingsbury C1Kingston B5Kingswood D6Knightsbridge C3Knockholt G5

LLadbroke Grove C3Ladywell F5Lambeth North D4Lancaster Gate C3Langdon Park F3Latimer Road B3Lebanon Road E6Lee F5Leicester Square D3Lewisham F4

L continuedLeyton F2Leyton Midland Road F2Leytonstone G2Leytonstone High Road G2Limehouse F3Liverpool Street E3Lloyd Park E6London Bridge D4London City Airport G4London Fields F2Loughborough Junction D4Loughton G1Lower Sydenham F5

MMaida Vale C2Malden Manor B5Manor House E2

M continuedManor Park G2Mansion House D3Marble Arch C3Maryland F2Marylebone C3Maze Hill F4Merton Park C5Mile End F3Mill Hill Broadway C1Mill Hill East D1Mitcham C5Mitcham Eastfields D5Mitcham Junction C5Monument E3Moor Park A1Moorgate E3Morden C5Morden Road C5

M continuedMorden South C5Mornington Crescent D2Mortlake B4Motspur Park B5Mottingham G5Mudchute F4

NNeasden C2New Addington F6New Barnet E1New Beckenham F5Newbury Park G2New Cross E4New Cross Gate E4New Eltham G5New Malden B5New Southgate E1Norbiton B5

N continuedNorbury D5North Acton B3North Dulwich D5North Ealing B3Northfields A3North Greenwich F4North Harrow B1Northolt A2Northolt Park A2North Sheen B4Northumberland Park F1North Wembley B2Northwick Park B2Northwood B1Northwood Hills B1Norwood Junction E5Notting Hill Gate C3Nunhead E4

OOakleigh Park E1Oakwood E1Ockendon H2Old Street E3Orpington G5Osterley A4Oval D4Oxford Circus D3

PPaddington C3Palmers Green E1Park Royal B3Parsons Green C4Peckham Rye E4Penge East E5Penge West E5Perivale A2Petts Wood G5

P continuedPhipps Bridge C5Piccadilly Circus D3Pimlico C4Pinner B1Plaistow F3Plumstead G4Ponders End F1Pontoon Dock G3Poplar F3Preston Road C2Prince Regent G3Pudding Mill Lane F3Purfleet H3Purley E6Purley Oaks E6Putney C4Putney Bridge C4

QQueensbury C1Queen’s Park B2Queens Road Peckham E4Queenstown Road

(Battersea) C4Queensway C3

RRainham H3Ravensbourne F5Ravenscourt Park B3Rayners Lane B2Raynes Park B5Rectory Road F2Redbridge G2Reedham D6Reeves Corner D6Regent’s Park D3

R continuedRichmond B4Rickmansworth A1Riddlesdown E6Roding Valley G1Romford H2Rotherhithe E4Royal Albert G3Royal Oak C3Royal Victoria G3Ruislip A1Ruislip Gardens A2Ruislip Manor A1Russell Square D3

SSt. Helier C6St. James Street F2St. James’s Park C3

S continuedSt. Johns F4St. John’s Wood C2St. Margarets B4St. Mary Cray G5St. Pancras International D2St. Paul’s D3Sanderstead E6Sandilands E6Selhurst D5Seven Kings G2Seven Sisters F2Shadwell E3Shenfield H1Shepherd’s Bush C3Shepherd’s Bush Market B3Shoreditch High Street E3Shortlands F5

S continuedSidcup G5Silver Street F1Slade Green H4Sloane Square C3Snaresbrook G2South Acton B3Southall A3South Bermondsey E4Southbury F1South Croydon E6South Ealing B3Southfields C4South Greenford A2South Hampstead C2South Harrow B2Southgate E1South Kensington C3South Kenton B2

S continuedSouth Merton C5South Quay F4South Ruislip A2South Tottenham F2Southwark D4South Wimbledon C5South Woodford G2Stamford Brook B3Stamford Hill F2Stanmore C1Star Lane F3Stepney Green E3Stockwell D4Stoke Newington F2Stonebridge Park B2Stoneleigh C6Stratford F2Stratford High Street F3

S continuedStratford International F2Strawberry Hill A5Streatham D5Streatham Common D5Streatham Hill D5Sudbury & Harrow Road B2Sudbury Hill B2Sudbury Hill Harrow B2Sudbury Town B2Sundridge Park F5Surbiton B5Surrey Quays E4Sutton C6Sutton Common C6Swiss Cottage C2Sydenham E5Sydenham Hill E5Syon Lane A4

TTadworth D6Tattenham Corner D6Teddington A5Temple D3Thames Ditton B5Theobalds Grove F1Therapia Lane D5Theydon Bois G1Thornton Heath D5Tolworth B5Tooting C5Tooting Bec C5Tooting Broadway C5Tottenham Court Road D3Tottenham Hale F2Totteridge &

Whetstone D1

T continuedTower Gateway E3Tower Hill E3Tufnell Park D2Tulse Hill D5Turkey Street F1Turnham Green B3Turnpike Lane E2Twickenham A5

UUpminster H2Upminster Bridge H2Upney G3Upper Holloway D2Upper Warlingham E6Upton Park G3Uxbridge A1

VVauxhall C4Victoria C3

WWaddon D6Waddon Marsh D5Wallington D6Waltham Cross F1Walthamstow Central F2Walthamstow

Queen’s Road F2Wandle Park D5Wandsworth Common C4Wandsworth Road C4Wandsworth Town C4Wanstead G2Wanstead Park G2Wapping E3Warren Street D3

W continuedWarwick Avenue C3Waterloo D4Watford A1Watford High Street B1Watford Junction B1Welling G4Wellesley Road E6Wembley Park C2Wembley Stadium C2West Acton B3Wembley Central B2Westbourne Park C3West Brompton C4Westcombe Park F4West Croydon D6West Drayton A3West Dulwich E5West Ealing B3

W continuedWestferry F3West Finchley D1West Ham F3West Hampstead C2West Harrow B2West India Quay F3Westminster D3West Norwood D5West Ruislip A1West Kensington C3West Silvertown G3West Sutton C6West Wickham E6White City B3Whitechapel E3White Hart Lane F1Whitton A5Whyteleafe E6

W continuedWhyteleafe South E6Willesden Green C2Willesden Junction B2Wimbledon C5Wimbledon Chase C5Wimbledon Park C4Winchmore Hill E1Woodford G1Woodgrange Park G3Wood Green E1Wood Lane B3Woodmansterne D6Woodside E5Woodside Park D1Wood Street F1Woolwich Arsenal G4Woolwich Dockyard G4Worcester Park C6

SPECIAL FARES APPLYOyster PAYG and

Travelcards are notvalid on

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A B C D E F G H

A B C D E F G H

ChigwellRodingValley

Grange Hill

Enfield Lock

Waltham Cross †

Cheshunt †

Broxbourne †Crews Hill

Gordon Hill

Enfield Chase

Grange Park

Winchmore Hill

Palmers Green

Bowes Park

Southbury

† TheobaldsGrove

TurkeyStreet

Brimsdown

Ponders End

Amersham

Chalfont& Latimer

Rayners Lane

Greenford

PiccadillyCircus

Brixton

Herne Hill

TottenhamCourt Road

BowRoad

BowChurch

WoodLane

Harrow-on-the-Hill

EalingBroadway

NorthwickPark

NortholtPark

WembleyStadium

BrondesburyPark

EdgwareRoad

Plaistow East HamUptonPark

EmersonPark

PrestonRoad Wembley Park

Farringdon

Baker Street

Gospel Oak

NottingHill Gate

High StreetKensington

GoodgeStreet

Chorleywood

Rickmansworth

South Harrow

Hanger Lane

West Ruislip

Bushey

Harrow & Wealdstone

Wembley Central

Watford Junction

South Ruislip

HeathrowTerminals

1, 2, 3

Sudbury Hill

EalingCommon

Balham

Clapham High Street

Wimbledon

Clapham North

Hammersmith

Watford

Croxley

Moor Park

RuislipManor

Eastcote

Perivale

Ruislip

Northwood

NorthwoodHills

Pinner

North Harrow

Kilburn ParkMaida Vale

WarwickAvenue

WarrenStreet

Hillingdon

Uxbridge Ickenham

RuislipGardens

Northolt

Castle Bar Park

South Greenford

Drayton Green

West Harrow

Kensal Rise

Upper Holloway

CaledonianRoad &

Barnsbury

SouthTottenham

BethnalGreen

ShoreditchHigh Street

Hoxton

Rotherhithe

Wapping

Surrey Quays

Haggerston

KilburnHigh Road

SouthHampstead

Brondesbury

Sudbury &Harrow Road

Kensal GreenFinchley Road

Kentish TownWest Hampstead

Queen’s Park

EustonSquare Barbican

Sudbury Town

Alperton

Park Royal

North Ealing

Goldhawk Road

Watford High Street

Carpenders Park

Hatch End

Headstone Lane Stanmore

Canons Park

Queensbury

Kingsbury

High Barnet

Totteridge & Whetstone

Woodside Park

West Finchley

Cockfosters

Oakwood

Southgate

Arnos Grove

BoundsGreen

Finchley Central

East Finchley

Highgate

Archway

Tufnell Park

Camden Town

Alexandra Palace

HornseyBruce Grove

White Hart Lane

Silver Street

Edmonton Green

Bush HillPark

EnfieldTown

Harringay

Hadley Wood

New Barnet

Oakleigh Park

Hendon

Kenton

South Kenton

North Wembley

Stonebridge Park

Harlesden

Parsons Green

Pimlico

Putney Bridge

Battersea Park

East Putney

Southfields

Wimbledon Park

Shepherd’sBush Market

ChiswickPark

TurnhamGreen

StamfordBrook

Whitton

Kingston

Mortlake

HaydonsRoad

Putney WandsworthTown

RavenscourtPark

WestKensington

St. James’sPark

Southwark Canada Water

Bermondsey

MazeHill

Charlton

SouthEaling

Feltham

NorthSheen Barnes

Chiswick

Barnes Bridge

Ewell West

WandsworthCommon

WandsworthRoad

Selhurst

Norbury

KewBridge

FulwellHampton NorbitonHamptonWick

Teddington

CarshaltonBeeches

Eltham

New Eltham

Sidcup Bexley

TherapiaLane

AmpereWay

WestNorwood

Centrale

ChurchStreet

Sandilands

AvenueRoad

Shortlands BromleySouth

BeckenhamRoad

Wellesley Road

Waddon

Wallington

BeddingtonLane

WaddonMarsh

StreathamHill Gipsy Hill

WestDulwich

SydenhamHill

ReevesCorner

LebanonRoadGeorge Street

Denmark Hill Nunhead

ThamesDitton

HamptonCourt

SloaneSquare

Boston Manor

Osterley

Northfields

HounslowEast

HounslowCentral

HounslowWest

HattonCross

Isleworth

HeathrowTerminal 4

Twickenham

St. Margarets

Syon Lane

Brentford

Hyde Park Corner

Temple

Oval

Knightsbridge

HeathrowTerminal

5

SouthallHayes &

HarlingtonWest

DraytonWestEalingHanwell

ActonMainLine

ActonTown

ActonCentral

EastActon

Queensway MarbleArch

BondStreet

AldgateEast

Green Park

Blackfriars

OxfordCircus

Canary Wharf

Holborn

SouthActon

ClaphamCommon

Kennington

Borough

Clapham South East Dulwich

Queens Road Peckham

North DulwichTootingBec

TootingBroadway

Colliers Wood

WestActon

NorthActon

HollandPark

LancasterGate

BaronsCourt

GloucesterRoad

ChanceryLane

MansionHouse

Shepherd’sBush

LatimerRoad

Finchley Road& Frognal

Essex Road

Westbourne Park

Ladbroke Grove

Royal Oak

SouthKensington

Richmond

Earl’sCourt

Dollis Hill

WillesdenGreen

Kilburn

Neasden

Brent Cross

Hendon Central

Hampstead

Hampstead Heath

Kentish TownWest

WalthamstowQueen’s Road

LeytonMidland Road

CamdenRoad

Golders Green

Elstree & Borehamwood

Mill Hill Broadway

Cricklewood

Swiss Cottage

Bayswater

Hounslow

Kew Gardens

Gunnersbury FulhamBroadway

StrawberryHill

WorcesterPark

South Wimbledon

DundonaldRoad

Streatham

TulseHill

Caterham

Upper WarlinghamWhyteleafe South

Whyteleafe

Kenley

Stoneleigh

Belmont

Banstead

Carshalton

Hackbridge

Epsom Downs

Tadworth

Kingswood

Tattenham Corner

St. John’s Wood

MorningtonCrescent

CoventGarden

RussellSquare

London Fields

Clapton

Leytonstone

St. JamesStreet

Cambridge Heath

Bethnal Green

Stepney Green

Whitechapel

NorthGreenwichfor The O2

PuddingMill Lane

LeicesterSquare

Bank

St. Paul’s

Angel

Westferry

WestcombePark

WoolwichDockyard

AbbeyWood

PlumsteadDeptford

Blackheath Kidbrooke

Welling

Falconwood

Barnehurst

Bexleyheath

Mottingham

Lee

Bickley St. Mary Cray

AlbanyPark Crayford

BlackwallShadwellRoyal

VictoriaCustom Housefor ExCeL

Arsenal

Ilford

Manor Park

Seven Kings

Goodmayes

ChadwellHeath

Ockendon

ChaffordHundred

Gidea Park

Harold Wood

† Brentwood

† Shenfield

Upney

Becontree

DagenhamHeathway

Dagenham East

Elm Park

Hornchurch

UpminsterBridge

Buckhurst Hill

Leyton

Loughton

Debden

Theydon Bois

Epping

HackneyDowns

Holloway Road

Caledonian Road

Turnpike Lane

ManorHouse

Wood Green

Chingford

Highams Park

Wood Street

Angel Road

HarringayGreen LanesCrouch Hill

WalthamstowCentral

Old Street

Stratford

Mile End

Devons Road

Deptford Bridge

Elverson Road

Langdon Park

All Saints

Bromleyby-Bow

HackneyCentralCanonbury

DalstonKingsland

DalstonJunction

Homerton

HackneyWick

TottenhamHaleSeven Sisters

NorthumberlandPark

RedbridgeSnaresbrook

South Woodford

Woodford

Newbury Park

Barkingside

Fairlop

Hainault

LeytonstoneHigh Road

Wanstead Park

WoodgrangePark

Prince Regent

Royal Albert

Beckton Park

Cyprus

Gallions Reach

Erith

Slade Green

Belvedere

St. Johns

New Cross

Bellingham

Beckenham Hill

Hither Green

ElmsteadWoods

ChislehurstPenge East

Kent House

Beckton

Barking

Maryland ForestGate

DagenhamDock

Rainham Purfleet Grays

EastIndia

UpminsterRomford

Anerley

Penge West

Lower Sydenham

MitchamEastfields

Raynes Park

New Malden

Cheam

Purley Oaks

Berrylands

Surbiton

Earlsfield

QueenstownRoad (Battersea)

Euston

Moorgate

St. PancrasInter-

national

Fenchurch Street

King’sCross

LiverpoolStreet

Marylebone

Victoria

Waterlooand

Waterloo East

Ewell East

Morden

Brockley

New Cross Gate

SouthBermondsey

Honor Oak Park

Forest Hill

Sydenham

Elephant & Castle

Stockwell

Vauxhall

MitchamJunction

Morden Road

Phipps Bridge

Belgrave Walk

Mitcham

Riddlesdown New Addington

King Henry’s Drive

Addington Village

Coombe Lane

Sanderstead

Wandle Park

Thornton Heath

StreathamCommon

GreatPortland

Street

White City

Kensington(Olympia)

West IndiaQuay

London City Airport

King George VSouth Quay

Crossharbour

Heron Quays

MudchuteIsland Gardens

Cutty Sark forMaritime Greenwich

Ladywell

Bromley North

Sundridge Park

Poplar

WestSilvertown

EmiratesRoyal Docks

EmiratesGreenwichPeninsula

Pontoon Dock

Crofton Park

PettsWood

Chelsfield

Knockholt

Ravensbourne

CannonStreet

Fieldway

Gravel Hill

Lloyd Park

Addiscombe

Blackhorse Lane

Woodside

Arena

HarringtonRoad

Clock House

New Beckenham

Eden Park

West Wickham

Hayes

Elmers End

Stamford Hill

Rectory Road

Stoke Newington

Regent’sPark

DraytonPark

LambethNorth

Wanstead Gants Hill

CityThameslink

Aldgate

EdgwareRoad

Monument TowerGateway

Westminster

Embankment

Finsbury Park

Limehouse

BlackhorseRoad

CanningTown

CharingCross

LondonBridge

Peckham Rye

West Ham

Chesham

TootingWimbledonChase

Paddington

Greenwich

WestBrompton

Imperial Wharf

Clapham Junction

CrystalPalace

Birkbeck BeckenhamJunction

WoolwichArsenal

Lewisham

Catford Catford Bridge

Orpington

Chessington South

Chessington North

Tolworth

MaldenManor

MotspurPark

South Merton

Morden South

St. Helier

Sutton Common

West Sutton

Grove Park

Purley

Edgware

Burnt Oak

Colindale

Belsize Park

Mill Hill East

Chalk Farm

New Southgate

Sudbury HillHarrow

Willesden Junction

Sutton

Highbury &Islington

Merton Park

LoughboroughJunction

TowerHill

StratfordInternational

NorwoodJunction

EastCroydon

South Croydon

West Croydon

Woodmansterne ReedhamCoulsdon Town

Chipstead

Coulsdon South

Star Lane

Abbey Road

StratfordHigh Street

TowardsEbbsfleet

International

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Key to lines and symbols

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Oyster pay as you go fares are available between all stationswithin the black broken line but NOT including travel on:• Southeastern high speed, • Heathrow Express and • Heathrow Connect between Hayes & Harlington and Heathrow.

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Rail & Tube QR 24/10/2012 11:20 Page 1


http://www.nationalrail.co.uk/passenger_services/maps/ 6 / 33

http://www.nationalrail.co.uk/passenger_services/maps/


A network. . .

7 / 33


The internet(By night!)

http://en.wikipedia.org/wiki/Internet_map8 / 33

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



Network models

I Individuals are considered as nodes (‘vertices’) on a network.

I Properties of nodes are associated with variables.

I Links (‘edges’): interactions between individuals.

I Dynamical equations/rules determine time-evolution.

A =

0 1 0 0 1 01 0 1 0 1 00 1 0 1 0 00 0 1 0 1 11 1 0 1 0 00 0 0 1 0 0

I Adjacency matrix can be used to give information about importance of

nodes/links — “centrality measures”

I Google’s PageRank c© uses eigenvectors.

9 / 33



Types of network model

I Regular lattice:

⊕ e.g. city-like geography,

⊕ can have high clustering,

long path-lengths l ∝ d1/D .

I Random (Erdos Renyı):

⊕ short path lengths l ∝ log Nlog k

,

no clustering (N →∞).

10 / 33



“Complex” networks

I Different models reproduce different features.

(a)

(b) (c)

Figure: (a): A small world network with random rewiring of a regular lattice.

(b): A preferential attachment graph which has a scale-free degree distribution.(c): A simple model of weakly-connected communities.

11 / 33





(a) (b)

(c)

Figure: (a): A small world network with random rewiring of a regular lattice.(b): A preferential attachment graph which has a scale-free degree distribution.

(c): A simple model of weakly-connected communities.

11 / 33





(a) (b) (c)

Figure: (a): A small world network with random rewiring of a regular lattice.(b): A preferential attachment graph which has a scale-free degree distribution.(c): A simple model of weakly-connected communities.

11 / 33



Why do networks matter?

“Braess’ paradox” for traffic flow:

Figure: From: http://en.wikipedia.org/wiki/Braess’s_paradox

I Solid lines: Constant (slow) roads.

I Dashed lines: Variable (fast) lines, depends on traffic density.

12 / 33

http://en.wikipedia.org/wiki/Braess's_paradox



Real-world relevance

I Mathematical results have shown that Braess’ paradox is about as likelyto occur as not occur in random additions to random networks.

I In Seoul a motorway closure resulted in traffic speeding up around thecity.

I In Stuttgart traffic improved after a section of road was closed for traffic.

I The closing of 42nd street in New York City reduced the amount ofcongestion.

I Studies have indicated routes in Boston, New York City and London thatcould be closed to reduce predicted travel times.

I Simulations have shown the effect in decentralized generation powertransmission networks.

From: http://en.wikipedia.org/wiki/Braess’s_paradox.

13 / 33

http://en.wikipedia.org/wiki/Braess's_paradox



Interconnected Urban Networks

Figure: c© Leonardo Dueas–Osorio.From: https://simonsfoundation.org/features/science-news/treading-softly-in-a-connected-world/

AAbbey Road F3Abbey Wood G4Acton Central B3Acton Main Line B3Acton Town B3Addington Village E6Addiscombe E6Albany Park G5Aldgate E3Aldgate East E3Alexandra Palace E1All Saints F3Alperton B2Amersham A1Ampere Way D5Anerley E5Angel E3Angel Road F1Archway D2Arena E5Arnos Grove E1Arsenal E2Avenue Road F5

BBaker Street C3Balham C5Bank E3Banstead C6Barbican D3Barking G3Barkingside G2Barnehurst H4Barnes C4Barnes Bridge B4Barons Court C3Battersea Park C4Bayswater C3Beckenham Hill F5Beckenham Junction F5Beckenham Road F5Beckton G4Beckton Park G3Becontree H2Beddington Lane D5Belgrave Walk C5Bellingham F5Belmont C6Belsize Park D2Belvedere G4Bermondsey E4Berrylands B5Bethnal Green (LU) E3Bethnal Green

(Greater Anglia) E3Bexley G5Bexleyheath G4Bickley G5Birkbeck E5Blackfriars D3Blackheath F4Blackhorse Lane E6Blackhorse Road F2Blackwall F3Bond Street C3Borough D4Boston Manor A3Bounds Green E1Bow Church F3Bowes Park E1Bow Road F3Brent Cross C2Brentford B4Brentwood H1Brimsdown F1Brixton D4Brockley E4Bromley-by-Bow F3Bromley North F5Bromley South F5Brondesbury C2Brondesbury Park C2Broxbourne F1Bruce Grove F2Buckhurst Hill G1Burnt Oak C1Bushey B1Bush Hill Park F1

CCaledonian Road E2Caledonian Road

& Barnsbury E2Cambridge Heath E2Camden Road D2Camden Town D2Canada Water E4Canary Wharf F4Canning Town F3Cannon Street E3Canonbury E2Canons Park C1Carpenders Park B1Carshalton D6Carshalton Beeches D6Castle Bar Park A3Caterham E6Catford F5Catford Bridge F5Centrale D6Chadwell Heath H2Chafford Hundred H2Chalfont & Latimer A1Chalk Farm D2Chancery Lane D3Charing Cross D3Charlton G4Cheam C6

C continuedChelsfield G5Chesham A1Cheshunt F1Chessington North B6Chessington South B6Chigwell G1Chingford F1Chipstead D6Chislehurst G5Chiswick B4Chiswick Park B3Chorleywood A1Church Street D6City Thameslink D3Clapham Common D4Clapham High Street D4Clapham Junction C4Clapham North D4Clapham South D4Clapton F2Clock House F5Cockfosters E1Colindale C1Colliers Wood C5Coombe Lane E6Coulsdon South D6Coulsdon Town D6Covent Garden D3Crayford H5Crews Hill E1Cricklewood C2Crofton Park F5Crossharbour F4Crouch Hill E2Croxley A1Crystal Palace E5Custom House for

ExCeL G3Cutty Sark for

Maritime Greenwich F4Cyprus G3

DDagenham Dock H3Dagenham East H2Dagenham Heathway H2Dalston Junction E2Dalston Kingsland E2Debden G1Denmark Hill D4Deptford F4Deptford Bridge F4Devons Road F3Dollis Hill C2Drayton Green A3Drayton Park E2Dundonald Road C5

EEaling Broadway B3Ealing Common B3Earl’s Court C3Earlsfield C4East Acton B3Eastcote B2East Croydon E6East Dulwich D4East Finchley D1East Ham G3East India F3East Putney C4Eden Park F5Edgware C1Edgware Road C3Edmonton Green F1Elephant & Castle D4Elmers End F5Elm Park H2Elmstead Woods G5Elstree &

Borehamwood C1Eltham G4Elverson Road F4Embankment D3Emerson Park H2Emirates Greenwich

Peninsula F4Emirates Royal Docks G3Enfield Chase E1Enfield Lock F1Enfield Town F1Epping G1Epsom Downs C6Erith H4Essex Road E3Euston D3Euston Square D3Ewell East C6Ewell West C6

FFairlop G2Falconwood G4Farringdon D3Feltham A5Fenchurch Street E3Fieldway F6Finchley Central D1Finchley Road C2Finchley Road & Frognal C2Finsbury Park E2Forest Gate G2Forest Hill E5Fulham Broadway C4Fulwell A5

GGallions Reach G3Gants Hill G2George Street E6Gidea Park H2

G continuedGipsy Hill D5Gloucester Road C3Golders Green D2Goldhawk Road B3Goodge Street D3Goodmayes G2Gordon Hill E1Gospel Oak D2Grange Hill G1Grange Park E1Gravel Hill E6Grays H3Great Portland Street D3Greenford A2Green Park C3Greenwich F4Grove Park F5Gunnersbury B4

HHackbridge D6Hackney Central F2Hackney Downs F2Hackney Wick F2Hadley Wood E1Haggerston E3Hainault G1Hammersmith B3Hampstead D2Hampstead Heath D2Hampton A5Hampton Court A5Hampton Wick B5Hanger Lane B3Hanwell A3Harlesden B2Harold Wood H2Harringay E2Harringay Green Lanes E2Harrington Road E5Harrow & Wealdstone B1Harrow-on-the-Hill B2Hatch End B1Hatton Cross A4Haydons Road C5Hayes E6Hayes & Harlington A3Headstone Lane B1Heathrow

Terminals 1, 2, 3 A4Heathrow Terminal 4 A4Heathrow Terminal 5 A4Hendon C2Hendon Central C2Herne Hill D5Heron Quays F4Highams Park F1High Barnet D1Highbury & Islington E2Highgate D2High Street Kensington C3Hillingdon A1Hither Green F5Holborn D3Holland Park C3Holloway Road E2Homerton F2Honor Oak Park E5Hornchurch H2Hornsey E2Hounslow A4Hounslow Central A4Hounslow East A4Hounslow West A4Hoxton E3Hyde Park Corner C3

IIckenham A1Ilford G2Imperial Wharf C4Island Gardens F4Isleworth A4

KKenley E6Kennington D4Kensal Green B2Kensal Rise C2Kensington (Olympia) C3Kent House E5Kentish Town D2Kentish Town West D2Kenton B1Kew Bridge B4Kew Gardens B4Kidbrooke F4Kilburn C2Kilburn High Road C2Kilburn Park C2King George V G4King Henry’s Drive F6King’s Cross D3Kingsbury C1Kingston B5Kingswood D6Knightsbridge C3Knockholt G5

LLadbroke Grove C3Ladywell F5Lambeth North D4Lancaster Gate C3Langdon Park F3Latimer Road B3Lebanon Road E6Lee F5Leicester Square D3Lewisham F4

L continuedLeyton F2Leyton Midland Road F2Leytonstone G2Leytonstone High Road G2Limehouse F3Liverpool Street E3Lloyd Park E6London Bridge D4London City Airport G4London Fields F2Loughborough Junction D4Loughton G1Lower Sydenham F5

MMaida Vale C2Malden Manor B5Manor House E2

M continuedManor Park G2Mansion House D3Marble Arch C3Maryland F2Marylebone C3Maze Hill F4Merton Park C5Mile End F3Mill Hill Broadway C1Mill Hill East D1Mitcham C5Mitcham Eastfields D5Mitcham Junction C5Monument E3Moor Park A1Moorgate E3Morden C5Morden Road C5

M continuedMorden South C5Mornington Crescent D2Mortlake B4Motspur Park B5Mottingham G5Mudchute F4

NNeasden C2New Addington F6New Barnet E1New Beckenham F5Newbury Park G2New Cross E4New Cross Gate E4New Eltham G5New Malden B5New Southgate E1Norbiton B5

N continuedNorbury D5North Acton B3North Dulwich D5North Ealing B3Northfields A3North Greenwich F4North Harrow B1Northolt A2Northolt Park A2North Sheen B4Northumberland Park F1North Wembley B2Northwick Park B2Northwood B1Northwood Hills B1Norwood Junction E5Notting Hill Gate C3Nunhead E4

OOakleigh Park E1Oakwood E1Ockendon H2Old Street E3Orpington G5Osterley A4Oval D4Oxford Circus D3

PPaddington C3Palmers Green E1Park Royal B3Parsons Green C4Peckham Rye E4Penge East E5Penge West E5Perivale A2Petts Wood G5

P continuedPhipps Bridge C5Piccadilly Circus D3Pimlico C4Pinner B1Plaistow F3Plumstead G4Ponders End F1Pontoon Dock G3Poplar F3Preston Road C2Prince Regent G3Pudding Mill Lane F3Purfleet H3Purley E6Purley Oaks E6Putney C4Putney Bridge C4

QQueensbury C1Queen’s Park B2Queens Road Peckham E4Queenstown Road

(Battersea) C4Queensway C3

RRainham H3Ravensbourne F5Ravenscourt Park B3Rayners Lane B2Raynes Park B5Rectory Road F2Redbridge G2Reedham D6Reeves Corner D6Regent’s Park D3

R continuedRichmond B4Rickmansworth A1Riddlesdown E6Roding Valley G1Romford H2Rotherhithe E4Royal Albert G3Royal Oak C3Royal Victoria G3Ruislip A1Ruislip Gardens A2Ruislip Manor A1Russell Square D3

SSt. Helier C6St. James Street F2St. James’s Park C3

S continuedSt. Johns F4St. John’s Wood C2St. Margarets B4St. Mary Cray G5St. Pancras International D2St. Paul’s D3Sanderstead E6Sandilands E6Selhurst D5Seven Kings G2Seven Sisters F2Shadwell E3Shenfield H1Shepherd’s Bush C3Shepherd’s Bush Market B3Shoreditch High Street E3Shortlands F5

S continuedSidcup G5Silver Street F1Slade Green H4Sloane Square C3Snaresbrook G2South Acton B3Southall A3South Bermondsey E4Southbury F1South Croydon E6South Ealing B3Southfields C4South Greenford A2South Hampstead C2South Harrow B2Southgate E1South Kensington C3South Kenton B2

S continuedSouth Merton C5South Quay F4South Ruislip A2South Tottenham F2Southwark D4South Wimbledon C5South Woodford G2Stamford Brook B3Stamford Hill F2Stanmore C1Star Lane F3Stepney Green E3Stockwell D4Stoke Newington F2Stonebridge Park B2Stoneleigh C6Stratford F2Stratford High Street F3

S continuedStratford International F2Strawberry Hill A5Streatham D5Streatham Common D5Streatham Hill D5Sudbury & Harrow Road B2Sudbury Hill B2Sudbury Hill Harrow B2Sudbury Town B2Sundridge Park F5Surbiton B5Surrey Quays E4Sutton C6Sutton Common C6Swiss Cottage C2Sydenham E5Sydenham Hill E5Syon Lane A4

TTadworth D6Tattenham Corner D6Teddington A5Temple D3Thames Ditton B5Theobalds Grove F1Therapia Lane D5Theydon Bois G1Thornton Heath D5Tolworth B5Tooting C5Tooting Bec C5Tooting Broadway C5Tottenham Court Road D3Tottenham Hale F2Totteridge &

Whetstone D1

T continuedTower Gateway E3Tower Hill E3Tufnell Park D2Tulse Hill D5Turkey Street F1Turnham Green B3Turnpike Lane E2Twickenham A5

UUpminster H2Upminster Bridge H2Upney G3Upper Holloway D2Upper Warlingham E6Upton Park G3Uxbridge A1

VVauxhall C4Victoria C3

WWaddon D6Waddon Marsh D5Wallington D6Waltham Cross F1Walthamstow Central F2Walthamstow

Queen’s Road F2Wandle Park D5Wandsworth Common C4Wandsworth Road C4Wandsworth Town C4Wanstead G2Wanstead Park G2Wapping E3Warren Street D3

W continuedWarwick Avenue C3Waterloo D4Watford A1Watford High Street B1Watford Junction B1Welling G4Wellesley Road E6Wembley Park C2Wembley Stadium C2West Acton B3Wembley Central B2Westbourne Park C3West Brompton C4Westcombe Park F4West Croydon D6West Drayton A3West Dulwich E5West Ealing B3

W continuedWestferry F3West Finchley D1West Ham F3West Hampstead C2West Harrow B2West India Quay F3Westminster D3West Norwood D5West Ruislip A1West Kensington C3West Silvertown G3West Sutton C6West Wickham E6White City B3Whitechapel E3White Hart Lane F1Whitton A5Whyteleafe E6

W continuedWhyteleafe South E6Willesden Green C2Willesden Junction B2Wimbledon C5Wimbledon Chase C5Wimbledon Park C4Winchmore Hill E1Woodford G1Woodgrange Park G3Wood Green E1Wood Lane B3Woodmansterne D6Woodside E5Woodside Park D1Wood Street F1Woolwich Arsenal G4Woolwich Dockyard G4Worcester Park C6


Travelcards are notvalid on

Heathrow Connectbetween

Hayes & Harlingtonand Heathrow Airport

or on Heathrow Express.


Travelcards are notvalid on Southeastern

high speed.For details, visit

southeasternrailway.co.uk

RenamedCoulsdon Townon 12th April.

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River Thames

River Thames

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A B C D E F G H

A B C D E F G H

ChigwellRodingValley

Grange Hill

Enfield Lock

Waltham Cross †

Cheshunt †

Broxbourne †Crews Hill

Gordon Hill

Enfield Chase

Grange Park

Winchmore Hill

Palmers Green

Bowes Park

Southbury

† TheobaldsGrove

TurkeyStreet

Brimsdown

Ponders End

Amersham

Chalfont& Latimer

Rayners Lane

Greenford

PiccadillyCircus

Brixton

Herne Hill

TottenhamCourt Road

BowRoad

BowChurch

WoodLane

Harrow-on-the-Hill

EalingBroadway

NorthwickPark

NortholtPark

WembleyStadium

BrondesburyPark

EdgwareRoad

Plaistow East HamUptonPark

EmersonPark

PrestonRoad Wembley Park

Farringdon

Baker Street

Gospel Oak

NottingHill Gate

High StreetKensington

GoodgeStreet

Chorleywood

Rickmansworth

South Harrow

Hanger Lane

West Ruislip

Bushey

Harrow & Wealdstone

Wembley Central

Watford Junction

South Ruislip

HeathrowTerminals

1, 2, 3

Sudbury Hill

EalingCommon

Balham

Clapham High Street

Wimbledon

Clapham North

Hammersmith

Watford

Croxley

Moor Park

RuislipManor

Eastcote

Perivale

Ruislip

Northwood

NorthwoodHills

Pinner

North Harrow

Kilburn ParkMaida Vale

WarwickAvenue

WarrenStreet

Hillingdon

Uxbridge Ickenham

RuislipGardens

Northolt

Castle Bar Park

South Greenford

Drayton Green

West Harrow

Kensal Rise

Upper Holloway

CaledonianRoad &

Barnsbury

SouthTottenham

BethnalGreen

ShoreditchHigh Street

Hoxton

Rotherhithe

Wapping

Surrey Quays

Haggerston

KilburnHigh Road

SouthHampstead

Brondesbury

Sudbury &Harrow Road

Kensal GreenFinchley Road

Kentish TownWest Hampstead

Queen’s Park

EustonSquare Barbican

Sudbury Town

Alperton

Park Royal

North Ealing

Goldhawk Road

Watford High Street

Carpenders Park

Hatch End

Headstone Lane Stanmore

Canons Park

Queensbury

Kingsbury

High Barnet

Totteridge & Whetstone

Woodside Park

West Finchley

Cockfosters

Oakwood

Southgate

Arnos Grove

BoundsGreen

Finchley Central

East Finchley

Highgate

Archway

Tufnell Park

Camden Town

Alexandra Palace

HornseyBruce Grove

White Hart Lane

Silver Street

Edmonton Green

Bush HillPark

EnfieldTown

Harringay

Hadley Wood

New Barnet

Oakleigh Park

Hendon

Kenton

South Kenton

North Wembley

Stonebridge Park

Harlesden

Parsons Green

Pimlico

Putney Bridge

Battersea Park

East Putney

Southfields

Wimbledon Park

Shepherd’sBush Market

ChiswickPark

TurnhamGreen

StamfordBrook

Whitton

Kingston

Mortlake

HaydonsRoad

Putney WandsworthTown

RavenscourtPark

WestKensington

St. James’sPark

Southwark Canada Water

Bermondsey

MazeHill

Charlton

SouthEaling

Feltham

NorthSheen Barnes

Chiswick

Barnes Bridge

Ewell West

WandsworthCommon

WandsworthRoad

Selhurst

Norbury

KewBridge

FulwellHampton NorbitonHamptonWick

Teddington

CarshaltonBeeches

Eltham

New Eltham

Sidcup Bexley

TherapiaLane

AmpereWay

WestNorwood

Centrale

ChurchStreet

Sandilands

AvenueRoad

Shortlands BromleySouth

BeckenhamRoad

Wellesley Road

Waddon

Wallington

BeddingtonLane

WaddonMarsh

StreathamHill Gipsy Hill

WestDulwich

SydenhamHill

ReevesCorner

LebanonRoadGeorge Street

Denmark Hill Nunhead

ThamesDitton

HamptonCourt

SloaneSquare

Boston Manor

Osterley

Northfields

HounslowEast

HounslowCentral

HounslowWest

HattonCross

Isleworth

HeathrowTerminal 4

Twickenham

St. Margarets

Syon Lane

Brentford

Hyde Park Corner

Temple

Oval

Knightsbridge

HeathrowTerminal

5

SouthallHayes &

HarlingtonWest

DraytonWestEalingHanwell

ActonMainLine

ActonTown

ActonCentral

EastActon

Queensway MarbleArch

BondStreet

AldgateEast

Green Park

Blackfriars

OxfordCircus

Canary Wharf

Holborn

SouthActon

ClaphamCommon

Kennington

Borough

Clapham South East Dulwich

Queens Road Peckham

North DulwichTootingBec

TootingBroadway

Colliers Wood

WestActon

NorthActon

HollandPark

LancasterGate

BaronsCourt

GloucesterRoad

ChanceryLane

MansionHouse

Shepherd’sBush

LatimerRoad

Finchley Road& Frognal

Essex Road

Westbourne Park

Ladbroke Grove

Royal Oak

SouthKensington

Richmond

Earl’sCourt

Dollis Hill

WillesdenGreen

Kilburn

Neasden

Brent Cross

Hendon Central

Hampstead

Hampstead Heath

Kentish TownWest

WalthamstowQueen’s Road

LeytonMidland Road

CamdenRoad

Golders Green

Elstree & Borehamwood

Mill Hill Broadway

Cricklewood

Swiss Cottage

Bayswater

Hounslow

Kew Gardens

Gunnersbury FulhamBroadway

StrawberryHill

WorcesterPark

South Wimbledon

DundonaldRoad

Streatham

TulseHill

Caterham

Upper WarlinghamWhyteleafe South

Whyteleafe

Kenley

Stoneleigh

Belmont

Banstead

Carshalton

Hackbridge

Epsom Downs

Tadworth

Kingswood

Tattenham Corner

St. John’s Wood

MorningtonCrescent

CoventGarden

RussellSquare

London Fields

Clapton

Leytonstone

St. JamesStreet

Cambridge Heath

Bethnal Green

Stepney Green

Whitechapel

NorthGreenwichfor The O2

PuddingMill Lane

LeicesterSquare

Bank

St. Paul’s

Angel

Westferry

WestcombePark

WoolwichDockyard

AbbeyWood

PlumsteadDeptford

Blackheath Kidbrooke

Welling

Falconwood

Barnehurst

Bexleyheath

Mottingham

Lee

Bickley St. Mary Cray

AlbanyPark Crayford

BlackwallShadwellRoyal

VictoriaCustom Housefor ExCeL

Arsenal

Ilford

Manor Park

Seven Kings

Goodmayes

ChadwellHeath

Ockendon

ChaffordHundred

Gidea Park

Harold Wood

† Brentwood

† Shenfield

Upney

Becontree

DagenhamHeathway

Dagenham East

Elm Park

Hornchurch

UpminsterBridge

Buckhurst Hill

Leyton

Loughton

Debden

Theydon Bois

Epping

HackneyDowns

Holloway Road

Caledonian Road

Turnpike Lane

ManorHouse

Wood Green

Chingford

Highams Park

Wood Street

Angel Road

HarringayGreen LanesCrouch Hill

WalthamstowCentral

Old Street

Stratford

Mile End

Devons Road

Deptford Bridge

Elverson Road

Langdon Park

All Saints

Bromleyby-Bow

HackneyCentralCanonbury

DalstonKingsland

DalstonJunction

Homerton

HackneyWick

TottenhamHaleSeven Sisters

NorthumberlandPark

RedbridgeSnaresbrook

South Woodford

Woodford

Newbury Park

Barkingside

Fairlop

Hainault

LeytonstoneHigh Road

Wanstead Park

WoodgrangePark

Prince Regent

Royal Albert

Beckton Park

Cyprus

Gallions Reach

Erith

Slade Green

Belvedere

St. Johns

New Cross

Bellingham

Beckenham Hill

Hither Green

ElmsteadWoods

ChislehurstPenge East

Kent House

Beckton

Barking

Maryland ForestGate

DagenhamDock

Rainham Purfleet Grays

EastIndia

UpminsterRomford

Anerley

Penge West

Lower Sydenham

MitchamEastfields

Raynes Park

New Malden

Cheam

Purley Oaks

Berrylands

Surbiton

Earlsfield

QueenstownRoad (Battersea)

Euston

Moorgate

St. PancrasInter-

national

Fenchurch Street

King’sCross

LiverpoolStreet

Marylebone

Victoria

Waterlooand

Waterloo East

Ewell East

Morden

Brockley

New Cross Gate

SouthBermondsey

Honor Oak Park

Forest Hill

Sydenham

Elephant & Castle

Stockwell

Vauxhall

MitchamJunction

Morden Road

Phipps Bridge

Belgrave Walk

Mitcham

Riddlesdown New Addington

King Henry’s Drive

Addington Village

Coombe Lane

Sanderstead

Wandle Park

Thornton Heath

StreathamCommon

GreatPortland

Street

White City

Kensington(Olympia)

West IndiaQuay

London City Airport

King George VSouth Quay

Crossharbour

Heron Quays

MudchuteIsland Gardens

Cutty Sark forMaritime Greenwich

Ladywell

Bromley North

Sundridge Park

Poplar

WestSilvertown

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https://simonsfoundation.org/features/science-news/treading-softly-in-a-connected-world/



Modelling innovation diffusion on networks

I Households are nodes on a network.I Innovation adoption or not are the variables.

I Links: interactions where people communicate informationwith each other about energy.

I Behaviour rules determine uptake dynamics.

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Threshold model dynamical rules

I Current adoption state, xi = 0, 1.

I Uptake based on perceived “usefulness” crossing a threshold:

future state: x ′i =

1 if xi = 1,1 if xi = 0 and ui > θi ,0 otherwise.

(1)

I θi : threshold (barriers, costs etc.)

16 / 33



Factors influencing uptake

Decisions to adopt can be based on various factors:

a) rational decision-making with regards to the intrinsic value ofa product;

b) social spreading of technology or ideas induced bypeer-to-peer communication of information;

c) interaction with the “mainstream” via a global feedback:I e.g. via media, markets etc.

17 / 33



Intrinsic benefit

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18 / 33



Social aspects of decision-making

I Decision of to adopt based on combination of factors:I personal + social benefit1.

I Intrinsic benefits to individual.I Social benefit combination of both2:

I personal social network – friends & neighbours,I mainstream social norm (society as a whole).

1: Delre et al., “Will it spread or not? the effects of social influences and network topology on innovationdiffusion.” Journal of Product Innovation Management (2010).

2: Valente, “Social network thresholds in the diffusion of innovations.” Social networks (1996).

19 / 33





I Intrinsic benefits to individual.

I Social benefit combination of both2:I personal social network – friends & neighbours,I mainstream social norm (society as a whole).



19 / 33





I Intrinsic benefits to individual.I Social benefit combination of both2:

I personal social network – friends & neighbours,I mainstream social norm (society as a whole).



19 / 33



Mathematical model

I Total utility to individual♠:

ui = αi pi + βi si + γi m (2)

I pi , si ,m: personal, peer-group and societal influence.I αi , βi , γi : relative weightings given to each factor,

I Different types of people have different αi , βi , γi —“archetypes”

♠ McCullen et al., “Multi-parameter models of innovation diffusion on complex networks”, SIADS (2013).

20 / 33



Real-world social networks

I Real networks have many features, including:I local connections, distant ties, wide spread in degrees,

community structure. . .

Figure: Inter-friend contacts on the Facebook website.

21 / 33



Random clustered model?

I Each node associated with G groups.

I Linked to L others in each group.

I Can also be linked to individuals in wider network.

I Can also impose geography.

?: Newman “Properties of highly clustered networks.” Physical Review E (2003).

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Simulation demonstration

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Outcomes — homogeneous archetypes

Expected chance of success depends on details:

t1 t2

t3 t4

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25 30 35 40

frac

tion

of a

dopt

ers

time (months)

24 / 33



Analysis of Results

I Given individuals have a certain θ, p, α, β, γ and m,require critical fraction of active neighbours:

s∗ =θ − αp − γm

β, (3)

I s∗ > 1: impossible,

I s∗ ≤ 0: immediate,

I 0 < s∗ ≤ 1: required number of active contacts:

Xi ≥ dki s∗e ≡ X ∗i , (4)

I combining (3) and (4) gives X ∗ regions of beta, γ plots. . .

25 / 33



Comparison with Watts-Strogatz

(a) 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

β

γ

WS, pr=0, N=500, -k=6

αp = θαp + γm0 = θ

mean fieldX*=1X*=2X*=3X*=4

0

0.2

0.4

0.6

0.8

1

aver

age

upta

ke

(c) 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

β

γ

Truss WS, pr=0.05, N=500, k=8 (2sw)



0

0.2

0.4

0.6

0.8

1

aver

age

upta

ke

(b) 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

β

γ

WS, pr=0.2, N=500, -k=6



0

0.2

0.4

0.6

0.8

1

aver

age

upta

ke

(d) 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

β

γ

Truss WS, pr=0.2, N=500, k=8 (2sw)



0

0.2

0.4

0.6

0.8

1

aver

age

upta

ke

Figure: (a) 1D k = 6, pr = 0, (b) 1D k = 6, pr = 0.2;(c) truss k = 8, pr = 0.05, (d) truss k = 8, pr = 0.2.

26 / 33



The Effect of Clustering

Clustering creates non-independent neighbourhoods:

(a) (b)

(c) (d)

I Only one “success” required in network for spreading to occur.

27 / 33



Clustering and Communities

Enhances expected uptake:

0

0.04

0.08

0.12

0.16

0.2

0.24

0.28

0.32

20 40 100 160

c

W

0.4 0.6 0.8 1_m(36)

Figure: Expected uptake for clustered random network, with number ofgroups W determining level of clustering c .

I Only one “success” required in network for spreading to occur.

28 / 33



Inputting real data

I Survey data including info on behaviours.

I Over 1050 valid responses received from residents of Leeds.

I Data used as a guide rather than definitive source,

I used to narrow choice of structure and parameter values,I also to illustrate potential applications.

Model element Parameter Question / Data

Network number of active individual Q. on who talks to/ group connections. whom about energy.

Threshold θ Q. on house type,tenancy and income.

Node archetypes α, β, γ Defra types of pro-enviro. behaviour

Bale, McCullen et al., Complexity (2014)

29 / 33



Modelling scenarios

I Different scenarios studied by varying dynamical modeland network parameters.

Baseline Seeded Community Incentives Snowball

Give efficiency Give efficiency Advertise a Recommend-a-Model Do Nothing measure to some measure to whole money off friend discountParam. (random) individuals communities. scheme. voucher scheme.

Links Data based – – – Increase

Threshold Data based – – Lower Lower

Initial Seed Unforced Random Target – –

Bale, McCullen at al., Energy Policy (2013)

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Comparison of model scenarios

Baseline Seeded Communities

Incentives Snowball

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Further reading

Research published in McCullen et al., “Multi-parameter models ofinnovation diffusion on complex networks”, SIADS (2013).:

and spreading via online networks. . .

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20150610 nick mccullen

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