Is bigger always better? How local online social networks can outperform global ones

Is bigger always better?How local online social networks

can outperform global ones

@[email protected]

Kaj Kolja Kleineberg Marian Boguña

When I was 13 years old...

Digital revolutionWe are the first generation of the

Information is the new oil

Information is the new oil

and

are theoilfields

You

all digital services need

Attentionbut our time is limited

The digital world forms a complexECOSYSTEM

with networks as competing species

Is b

igg

er

alw

ays

bett

er?

digital diversitySystem's level perspective:

possible?Is

Isolatedevolution of onlinesocial networks

Digital ecologyinteractingnetworks

World modelis bigger always

better?

Evolution of isolated networks

Motivation Isolated evolution Digital ecology World model Summary & outlook

The topological evolution of large quasi-isolated OSNexhibits a dynamical percolation transition

Dynamical percolation transition demands new classof growing network models.

12


The topological evolution of large quasi-isolated OSNexhibits a dynamical percolation transition

Dynamical percolation transition demands new classof growing network models.

12


The pre-existing underlying social structureforms the backbone of the evolution of the OSN

Online social network layer

Traditional contactnetwork layer

ActiveOnline & offline

PassiveOnline & offlineSusceptibleOnly offline

13


The pre-existing underlying social structureforms the backbone of the evolution of the OSN

Online social network layer

Traditional contactnetwork layer

ActiveOnline & offline

PassiveOnline & offlineSusceptibleOnly offline

Mass media activation Viral activation

Deactivation Viral reactivation

13


Model precisely reproduces the entire topological evolutionand reveals balance between virality and media influence

Model results ParametersGCC model

2nd comp. model

ASPL model x4

GCC Pokec

2nd comp. Pokec

ASPL Pokec x4

103 104 105 1060

20

40

60

80

100

120

140

N

Virality is about four timesstronger thanmass media

Interplay between virality andmass media dynamicsis the main underlying principle of the OSN evolution.

14




2nd comp. model

ASPL model x4

GCC Pokec

2nd comp. Pokec

ASPL Pokec x4

103 104 105 1060

20

40

60

80

100

120

140

N



14




2nd comp. model

ASPL model x4

GCC Pokec

2nd comp. Pokec

ASPL Pokec x4

103 104 105 1060

20

40

60

80

100

120

140

N



14


Below a critical value of the viral parameterthe network becomes entirely passive

Λc

0.00 0.02 0.04 0.06 0.08

0.00

0.05

0.10

0.15

0.20

0.25

Λ

ΡA

Our model predicts the survival and death of onlinesocial networks.

15


Below a critical value of the viral parameterthe network becomes entirely passive

Λc

0.00 0.02 0.04 0.06 0.08

0.00

0.05

0.10

0.15

0.20

0.25

Λ

ΡA

Our model predicts the survival and death of onlinesocial networks.

15


Evolution of the digital society revealsbalance between viral and mass media influence

Social structureprecedes OSNformation

Balanceof viral and massmedia influence

Survival and deathof networks

PRX 4, 031046, 2014

16






PRX 4, 031046, 2014

16






PRX 4, 031046, 2014

16

Digital ecology


Digital ecosystem is formed by multiple networkscompeting for the attention of individuals

OSN 2

OSN 1

Underl.network

ActivePassiveSusceptible

Partial states

Virality shareDistribution

between OSNsλi = ωi(ρ

a)λ

Rich-get-richermore active

networks obtainhigher share

Here: ωi = [ρai ]σ/

∑j [ρ

aj ]

σ

σ: activity affinity

Does rich-get-richer effect always lead to thedomination of a single network?

18



OSN 2

OSN 1

Underl.network


Partial states



a)λ




∑j [ρ

aj ]

σ



18



OSN 2

OSN 1

Underl.network


Partial states



a)λ




∑j [ρ

aj ]

σ



18



OSN 2

OSN 1

Underl.network


Partial states



a)λ




∑j [ρ

aj ]

σ



18



OSN 2

OSN 1

Underl.network


Partial states



a)λ




∑j [ρ

aj ]

σ



18


Nonlinear dynamics of network evolution enablecoexistence despite rich-get-richer mechanism

Meanfield approximation:

ρai = ρai

[λ ⟨k⟩ωi(ρ

a) [1− ρai ]− 1

]+

λ

νωi(ρ

a)ρsi

ρsi = −λ

νωi(ρ

a)ρsi

[1 + ν ⟨k⟩ ρai

]Weights:

ωi =[ρai ]

σ∑j [ρ

aj ]

σ

Activity affinity σ: how much more likely individuals are toengage in more active networks

19



StableUnstable

0.50 0.75 1.00 1.25 1.500.00

0.25

0.50

0.75

0.00

0.25

0.50

0.75

Bifurcation diagram

ρ1a

0.0 0.5 1.0 1.5

0.50

0.75

σ

σ

ρ1,2

a

Coexistencedespite rich-get-richer

Damageto diversity is irreversible

20



StableUnstable

0.50 0.75 1.00 1.25 1.500.00

0.25

0.50

0.75

0.00

0.25

0.50

0.75

Bifurcation diagram

ρ1a

0.0 0.5 1.0 1.5

0.50

0.75

σ

σ

ρ1,2

a



20



StableUnstable

0.50 0.75 1.00 1.25 1.500.00

0.25

0.50

0.75

0.00

0.25

0.50

0.75

Bifurcation diagram

ρ1a

0.0 0.5 1.0 1.5

0.50

0.75

σ

σ

ρ1,2

a



20


Maximum number of coexisting networksdepends on total virality and activity affinity

Overall attention to OSNs

Mor

e lik

ely

to e

ngag

ein

mor

e ac

tive

OS

Ns

Dom.2 coex.3 coex.4 coex.5 coex.

1 2 3 4 5 60.0

0.5

1.0

1.5

λ/λc1

σ

How many networks can coexist

Multiple networks can coexist despite rich-get-richermechanism.

21




Mor

e lik

ely

to e

ngag

ein

mor

e ac

tive

OS

Ns


1 2 3 4 5 60.0

0.5

1.0

1.5

λ/λc1

σ


3 networks

2 networks

1 network

Stable configurations


21




Mor

e lik

ely

to e

ngag

ein

mor

e ac

tive

OS

Ns


1 2 3 4 5 60.0

0.5

1.0

1.5

λ/λc1

σ


3 networks

2 networks

1 network

Stable configurations


21


Noise and shape of basin of attractionlimit observed digital diversity

Multi stabilityseveral stablefixed points

Noisein full dynamical

model

Dom.Coex.

2 4 6 8 100.0

0.4

0.8

1.2

λ/λc1

σ

Reachability for 2 networks

→ Effective critical lines for more networks saturate atsuccessively lower values σi,eff

c

Evenwithout precise knowledge of the empiricalparameters our theory explainsmoderate diversity.

22





model

Dom.Coex.

2 4 6 8 100.0

0.4

0.8

1.2

λ/λc1

σ



c


22





model

Dom.Coex.

2 4 6 8 100.0

0.4

0.8

1.2

λ/λc1

σ



c


22


Ecological theory of the digital world explains whywe observe a moderate number of coexisting networks

Coexistencedespite

rich-get-richer

Damageto diversity isirreversible

Moderatedigital diversity

observed

Sci. Rep. 5, 10268, 2015

23



Coexistencedespite

rich-get-richer



observed

Sci. Rep. 5, 10268, 2015

23



Coexistencedespite

rich-get-richer



observed

Sci. Rep. 5, 10268, 2015

23

World model


World map of social networks:The emergence of a single, prevalent »big brother«

Courtesy of Vincenzo Cosenza (www.vincos.it) 25


Intercountry social ties lead to an increasedintrinsic fitness of the international network

Competition Competition

Localnetwork 1

Localnetwork 2

Globalnetwork


Localnetwork 1

Localnetwork 2

Globalnetwork

Globalnetwork

Frequency of intercountrysocial ties

Coarse-grainedcoupling

Effective activityinternational network moreattractive (intercountry ties)

Air travelpassengersWij proxy forintercountry social ties

ρai,int = ρai,int + α∑

j =iΩijρaj,int Ωij ∝Wij/Ni

26




Localnetwork 1

Localnetwork 2

Globalnetwork


Localnetwork 1

Localnetwork 2

Globalnetwork

Globalnetwork






j =iΩijρaj,int

Ωij ∝Wij/Ni

26




Localnetwork 1

Localnetwork 2

Globalnetwork


Localnetwork 1

Localnetwork 2

Globalnetwork

Globalnetwork






j =iΩijρaj,int Ωij ∝Wij/Ni

26


Network of multi-layer networksrepresents global digital ecology


Partial states

Localnetwork

Globalnetwork

Effective activity

27


Double meanfield approximation describes mean activitieswith global connectivity as new control parameter

x =⟨ρai,loc

⟩: mean activity of local networks

y =⟨ρai,int

⟩: mean activity of international network

x = x

[λ ⟨k⟩ xσ

xσ + (y(1 + Ω))σ[1− x]− 1

]y = y

[λ ⟨k⟩ (y(1 + Ω))σ

xσ + (y(1 + Ω))σ[1− y]− 1

]Additional control parameter Ω = α ⟨Ωij⟩ (global connectivity)

28


Local networks can coexist, dominate, or become extinctdepending on global connectivity and activity affinity

0.4 0.6 0.80.0

0.2

0.4

0.6

0.8

σ

Ω

Phase diagramCoexistenceis possible

Coexistenceis impossible

Saddlenodebifurcation

Attractorswitching

Local attractsfrom

Glo

bal c

onne

ctiv

ity

Activity affinity

29



0.4 0.6 0.80.0

0.2

0.4

0.6

0.8

σ

Ω




Attractorswitching

Local attractsfrom

Glo

bal c

onne

ctiv

ity

0.0 0.2 0.4 0.6 0.80.0

0.2

0.4

0.6

0.8

x

y

0.0 0.2 0.4 0.6 0.80.0

0.2

0.4

0.6

0.8

x

y

0.0 0.2 0.4 0.6 0.80.0

0.2

0.4

0.6

0.8

x

y

International winsLocal networks winNetworks coexist 29



0.4 0.6 0.80.0

0.2

0.4

0.6

0.8

σ

Ω

Phase diagram

0.0 0.2 0.4 0.6 0.80.0

0.2

0.4

0.6

0.8

x

y

0.2 0.4 0.6 0.8

x

0.2 0.4 0.6 0.8

x

0.2 0.4 0.6 0.8

x

Initial condition

International winsLocal networks winNetworks coexist

Coexistenceis possible



Attractorswitching

Local attractsfrom

Glo

bal c

onne

ctiv

ity

29



0.4 0.6 0.80.0

0.2

0.4

0.6

0.8

σ

Ω




Attractorswitching

Local attractsfrom

Glo

bal c

onne

ctiv

ity

Activity affinity

Highest probability for extinction of local networks isat intermediate value of the activity affinity σ.

29


1:1000 scale model of the digital world is constructedwith synthetic networks for underlying social structure

Synthetic networksfor underlying societies

(S1model)

Launch timeInternational network starts

delayed except in US

Real topologyof the air travel network

Simulatefull stochastic model

30




(S1model)





30




(S1model)





30




(S1model)





30


Local networks always become extinct for intermediateactivity affinity but can survive otherwise

Relative prevalence of int. network: Φ =⟨

ρai,int

ρai,int+ρai,loc

⟩

31




ρai,int

ρai,int+ρai,loc

⟩

31




ρai,int

ρai,int+ρai,loc

⟩

31




ρai,int

ρai,int+ρai,loc

⟩

31




ρai,int

ρai,int+ρai,loc

⟩

31




ρai,int

ρai,int+ρai,loc

⟩

31


Empirical evolution: Which regiondoes it belong to?

Courtesy of Vincenzo Cosenza (www.vincos.it) 32


Estimation of most probable parametersby comparison with empirical data

Empirical datacountries where

local most popular

Time mappingmodel timescalearbitrarily fixed

Parametersthat provide best

agreement

EmpiricModel

2010 2012 20140

10

20

30

40

t

N

Local most popular

2004 2005 2006 2007

0.4

0.8

1.2

1.6

Year

Timestrech

Time mapping

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.5 1.0 1.5 2.00

1

2

3

4

5

σ

Δt

α=2.0

1.5

2.0

2.5

3.0

3.5

Year: 2006Strech: 0.6 : 15.3

33




local most popular



agreement

EmpiricModel

2010 2012 20140

10

20

30

40

t

N

Local most popular

2004 2005 2006 2007

0.4

0.8

1.2

1.6

Year

Timestrech

Time mapping

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.5 1.0 1.5 2.00

1

2

3

4

5

σ

Δt

α=2.0

1.5

2.0

2.5

3.0

3.5

Year: 2006Strech: 0.6 : 15.3

33




local most popular



agreement

EmpiricModel

2010 2012 20140

10

20

30

40

t

N

Local most popular

2004 2005 2006 2007

0.4

0.8

1.2

1.6

Year

Timestrech

Time mapping

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.5 1.0 1.5 2.00

1

2

3

4

5

σ

Δt

α=2.0

1.5

2.0

2.5

3.0

3.5

Year: 2006Strech: 0.6 : 15.3

33


Most probable parameters lie in coinflip regionimplying new interpretation of Facebook's takeover

A network like Facebook could have become extinctwith significant probability.

34



Inter-nationalwins

Localwins

70%

30%


34



Inter-nationalwins

Localwins

70%

30%


34


Bigger is not always better: local networks can persistbut they just were not lucky

Effective activityhigher intrinsic fitness ofinternational network

Local networkscan persist if launched earlier

under certain conditions

Coinflip regionfate of system up to chance

Empirical dataevidence for coinflip region

arxiv:1504.01368

35








arxiv:1504.01368

35








arxiv:1504.01368

35








arxiv:1504.01368

35

Summary & outlook


Multiscale theory of the digital world: From individual tiesto globally interacting networks

Individuals Interacting Worldwide

Mod

el Strength ofsocial ties

Res

ult Weak ties

have highertransmissibility

Viral + mediaeffect & under-lying structure

Viral effect is about fourtimes stronger

Rich-get-richer& diminishingreturns

Coexistance of amoderate numberof services

Network of net-works & effectiveactivity

Local networks canprevail under certainconditions

Focu

s

12

3

101 - 102 105 - 106 106 - 109 >109

Ord

er

Isolatednetwork networks

PRX 4, 031046 Sci. Rep. 5, 10268 arxiv:1504.01368 37




Mod


Res

ult Weak ties








Focu

s

12

3

101 - 102 105 - 106 106 - 109 >109

Ord

er


PRX 4, 031046 Sci. Rep. 5, 10268 arxiv:1504.01368 37




Mod


Res

ult Weak ties








Focu

s

12

3

101 - 102 105 - 106 106 - 109 >109

Ord

er


PRX 4, 031046 Sci. Rep. 5, 10268 arxiv:1504.01368 37




Mod


Res

ult Weak ties








Focu

s

12

3

101 - 102 105 - 106 106 - 109 >109

Ord

er


PRX 4, 031046 Sci. Rep. 5, 10268 arxiv:1504.01368 37

Digital diversity is possible- but so is its unrecoverable loss.

Just as a monopoly in economy is a threat to free markets, the lack of

poses a threat to the digital diversity

freedom of information.

Digital diversity is important. So write downthe references and contact information now!

References:

K.-K. Kleineberg, M. Boguña.PRX 4, 031046, 2014

K.-K. Kleineberg, M. Boguña.Sci. Rep. 5, 10268, 2015

K.-K. Kleineberg, M. Boguña.arxiv:1504.01368, 2015

Kaj Kolja Kleineberg:

• [email protected]

• @KoljaKleineberg

• koljakleineberg.wordpress.com

in • Kaj Kolja Kleineberg

Digital diversity is important. So write downthe references and contact information now!

References:

K.-K. Kleineberg, M. Boguña.PRX 4, 031046, 2014

K.-K. Kleineberg, M. Boguña.Sci. Rep. 5, 10268, 2015

K.-K. Kleineberg, M. Boguña.arxiv:1504.01368, 2015



• @KoljaKleineberg← Slides!


in • Kaj Kolja Kleineberg


CREDITS

brian: espressoSocial media chalk: mkhmarketing.wordpress.comObsolete hardware David Haywardoil field: Damian GadalCat attention: David CornejoCables: jerry johnNetwork "ring": Adam BeasleyBoxing gloves: Gabriele FumeroWorld: Lorenzo BaldiniMegaphone: Alex Auda SamoraBiohazard: Shailendra ChouhanLayer icon: MentaltoyBalance (scale) icon: Roman Kovbasyuk

Death symbol: Mila RedkoPie Chart: P.J. OnoriMoney sack: Lemon LiuTeam icon: Joshua JonesHand icon: irene hoffmanarm with muscle: Sergey KrivoyTime: Richard de VosLocal: Phil GoodwinSummary (article) icon: Stefan Parnarovflower: Nishanth JoisRead magazine: Evan TravelsteadGlobe 2: Ealancheliyan sdices: Drew Ellis



• @KoljaKleineberg


in • Kaj Kolja Kleineberg41

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Is bigger always better? How local online social networks can outperform global ones