A 1:1000 scale model of the digital world

When I was 13 years old...

Digital revolutionWe are the first generation of the

Information is the new oil

are theoilfields

all digital services need

Attentionbut our time is limited

The digital world forms a complexECOSYSTEM

with networks as competing species

Can we preserve digital diversity?

Evolution and ecology of online socialnetworks

Motivation Evolution and ecology of OSNs World model Summary & outlook

Evolution of isolated online social networks is governedby underlying social structure and two dynamical processes

Online social network layer

Traditional contactnetwork layer

ActiveOnline & offline

PassiveOnline & offlineSusceptibleOnly offline

Evolution of isolated online social networks is governedby underlying social structure and two dynamical processes

Online social network layer

Traditional contactnetwork layer

ActiveOnline & offline

PassiveOnline & offlineSusceptibleOnly offline

Mass media activation Viral activation

Deactivation Viral reactivation

Phys. Rev. X 4, 031046 10

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

Underl.network

ActivePassiveSusceptible

Partial states

Virality shareDistribution

between OSNsλi = ωi(ρ

Rich-get-richermore active

networks obtainhigher share

Here: ωi = [ρai ]σ/

∑j [ρ

aj ]σ

σ: activity affinity

Networks can coexist despite rich-get-richermechanism.

Sci. Rep. 5, 10268 • Tomorrow, 17:20, A5+A6

Underl.network

Partial states

∑j [ρ

aj ]σ

Underl.network

Partial states

∑j [ρ

aj ]σ

Underl.network

Partial states

∑j [ρ

aj ]σ

Underl.network

Partial states

∑j [ρ

aj ]σ

1:1000 scale model of the digital world

World map of social networks: Facebook takes overand how can we explain it?

Courtesy of Vincenzo Cosenza (www.vincos.it) 13

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

Competition Competition

Localnetwork 1

Localnetwork 2

Globalnetwork

Localnetwork 1

Localnetwork 2

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

Localnetwork 1

Localnetwork 2

Globalnetwork

Localnetwork 1

Localnetwork 2

Globalnetwork

j =iΩijρaj,int

Ωij ∝Wij/Ni

Localnetwork 1

Localnetwork 2

Globalnetwork

Localnetwork 1

Localnetwork 2

Globalnetwork

j =iΩijρaj,int Ωij ∝Wij/Ni

Network of multi-layer networks represents globaldigital ecology for the 80 largest countries

Partial states

Localnetwork

Globalnetwork

Effective activity

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

[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)

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

0.4 0.6 0.80.0

Phase diagramCoexistenceis possible

Coexistenceis impossible

Saddlenodebifurcation

Attractorswitching

Local attractsfrom

Activity affinity

0.4 0.6 0.80.0

Attractorswitching

Local attractsfrom

0.0 0.2 0.4 0.6 0.80.0

International winsLocal networks winNetworks coexist 17

0.4 0.6 0.80.0

Phase diagram

0.0 0.2 0.4 0.6 0.80.0

0.2 0.4 0.6 0.8

Initial condition

International winsLocal networks winNetworks coexist

Coexistenceis possible

Attractorswitching

Local attractsfrom

0.4 0.6 0.80.0

Attractorswitching

Local attractsfrom

Activity affinity

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

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

(S1model)

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

Mean prevalence of int. network: Φ =⟨

ρai,int

ρai,int+ρai,loc

ρai,int

ρai,int+ρai,loc

ρai,int

ρai,int+ρai,loc

ρai,int

ρai,int+ρai,loc

ρai,int

ρai,int+ρai,loc

ρai,int

ρai,int+ρai,loc

1:1000 scale model of the digital world revealsconditions for survival of local networks

Intercountry tieslead to intrinsic fitness

Heterogeneous fitnesscan impede coexistence

International networkalways dominates for

intermediate activity affinity

Local networkscan survive for low and high

activity affinity

arxiv:1504.01368

activity affinity

arxiv:1504.01368

activity affinity

arxiv:1504.01368

activity affinity

arxiv:1504.01368

Summary & outlook

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

Individuals Interacting Worldwide

el Strength ofsocial ties

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

101 - 102 105 - 106 106 - 109 >109

Isolatednetwork networks

PRX 4, 031046 Sci. Rep. 5, 10268 arxiv:1504.01368 22

ult Weak ties

101 - 102 105 - 106 106 - 109 >109

PRX 4, 031046 Sci. Rep. 5, 10268 arxiv:1504.01368 22

ult Weak ties

101 - 102 105 - 106 106 - 109 >109

PRX 4, 031046 Sci. Rep. 5, 10268 arxiv:1504.01368 22

ult Weak ties

101 - 102 105 - 106 106 - 109 >109

PRX 4, 031046 Sci. Rep. 5, 10268 arxiv:1504.01368 22

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 (tomorrow, 17:20, A5+A6)

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

Kaj Kolja Kleineberg:

• [email protected]

• @KoljaKleineberg

in • Kaj Kolja Kleineberg24

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 (tomorrow, 17:20, A5+A6)

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

• @KoljaKleineberg← Slides!

CREDITS

Social 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 KovbasyukDeath symbol: Mila Redko

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

Icons: thenounproject.com

• @KoljaKleineberg

A 1:1000 scale model of the digital world

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