evolution of the digital society reveals balance between viral and mass media influence

U

BUNIVERSITAT DE BARCELONA

Evolution of the Digital Society Reveals Balancebetween Viral and Mass Media Influence

September 23, 2014

Kaj Kolja KleinebergMarián Boguñá

Departament de Física FonamentalUniversitat de Barcelona

You are there

How does the structureof the social universe emerge?

We are here. But we are not there yet.

Motivation & introduction Case study Basic model Extended model Summary & Outlook

AGENDA

1. Case study

2. Basic model

3. Extended model

4. Summary & Outlook

3

CASE STUDY


TOPOLOGICAL EVOLUTION OF QUASI-ISOLATED OSN

Pokec slovakian OSN Dyn. percolation transition

Successful

Num

ber

of u

sers

1999 2012

>90% coverage(20 year old)

PopulationSlovakia per age

Users Pokec

Isolated (Language) GCC Pokec

2nd comp. Pokec

ASPL Pokec x4

103 104 105 1060

20

40

60

80

100

120

140

N

2000 2004 2008 20120.0

0.4

0.8

1.2

Year

Users in million

Dynamical percolation transition demands newclass of growing network models.

5

BASIC MODEL


THE FIRST SOCIAL NETWORK REPRESENTATION

Social networks existed long before online social networks.

7


TWO-LAYER DESIGN: THE SOCIAL BACKBONE

Online socialnetwork layer

Traditional contactnetwork layer

ActiveOnline & offline

PassiveOnline & offline

SusceptibleOnly offline

Mass media effect Viral activation

Deactivation Viral reactivation

8








Finalsnapshot

Empiricalevolution

Extractsnapshots

Empiricaldata

Modelevolution

Compare

Finalsnapshot

8








Finalsnapshot

Empiricalevolution

Extractsnapshots

Empiricaldata

Modelevolution

Compare

Finalsnapshot

Can we reproduce the empirical evolution

of the Pokec network?

8


RESULTS: MODEL & DATA

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.

9

EXTENDED MODEL


THE MICROSCOPIC PICTURE

Mean local clustering Results

Pokec

Basic model

103 104 105 106

0.00

0.05

0.10

0.15

0.20

N

Clustering

Local mechanism

Viral transmissibility-strengthrelation: λij ∝ λ [tie strength]η

N

Pokec

103 104 105 1060.00

0.05

0.10

0.15

0.20

Clustering

We find: η = −0.65

11


THE MICROSCOPIC PICTURE

Mean local clustering Results

Pokec

Basic model

103 104 105 106

0.00

0.05

0.10

0.15

0.20

N

Clustering

Local mechanism

Viral transmissibility-strengthrelation: λij ∝ λ [tie strength]η

N

Pokec

103 104 105 1060.00

0.05

0.10

0.15

0.20

Clustering

We find: η = −0.65

Individuals have a higher tendency to subscribe ifinvited byweaker social contacts.

11


COMPARISON BASIC & EXTENDED MODEL

Components

Assortativity

Mean degree

Mean local clustering

N N103 104 105 106

0.0

0.1

0.2

0.3

0

500

1000

1500

2000

2500

3000

103 104 105 1060.00

0.05

0.10

0.15

0.200

5

10

15

20

PokecBasic modelExtended model

Extended model performs well for global & localtopology.

12

SUMMARY & OUTLOOK


SUMMARY: TAKE HOME MESSAGES

- Two-parameter model reproduces entire topologicalevolution with unprecedented precision

- Coupling to underlying social structure essential tounderstand dynamical percolation transition

- Balance between viral andmass media influence governstopological evolution

- Individuals have a higher subscription probability if invitedbyweaker social contacts

- Outlook & applications:- Quasi-isolated OSN allows us to gauge fundamentalmechanisms- Model predicts survival and death of networks- Investigation of competition between online social networks

14


QUESTIONES, COMMENTS & MORE

L. Takac and M. Zabovsky.»Data analysis in public social networks.«International Scientific Conference and International Workshop PresentDay Trends of Innovations, 2012.Pokec data | Stanford Large Network Dataset Collection | Jure Leskovec

K. Kleineberg and M. Boguñá.»Evolution of the Digital Society Reveals Balance between Viral and MassMedia Influence«.Phys. Rev. X 4, 031046, 2014.

Please don't hesitate to contact me.Kaj Kolja [email protected]

15

APPENDIX

Appendix

STRENGTH OF WEAK TIES

It is argued that the degree of overlap of two individuals'friendship networks varies directly with the strength of theirtie to one another.

Granovetter, 1973

i j

sij = mij + 1 (1)

mij : Multiplicity (•) of link i− j

λij = λsηij⟨sηij

⟩ (2)

17

Appendix

TRANSMISSIBILITY-STRENGTH AND CLUSTERING

N

Mean local clustering Transmissibility-strength

Empiric transmissibility-strength coefficient

Basic model

PokecA B

Pokec

-0.8 -0.6 -0.4 -0.2 0.0 0.2

-0.04

-0.02

0.00

0.02

103 104 105 1060.00

0.05

0.10

0.15

0.20

Figure: Estimation of Transmissibility-strength relationship.

18

Appendix

SUSTAINED ACTIVITY

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

Figure: Sustained activity threshold λc ≈ 0.02.

19

Appendix

NULLMODEL

NullmodelPokec

103 104 105 1060

2

4

6

N comp in 1000

N

GCC Pok.2nd comp. Pok.

ASPL Pok. x4

GCC N.M.2nd comp. N.M.

ASPL N.M. x4

103 104 105 1060

50

100

150

200

N

Nullmodel and empiric network

Figure: Nullmodel with completely random subscriptions.

20

Appendix

BASIC AND EXTENDED: TOPOLOGICAL FEATURES

GCC 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

Basic model and empiric network

Figure: Basic model

GCC 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

Extended model and empiric network

Figure: Extended model

21

Appendix

BASIC AND EXTENDED: BALANCE OF MECHANISMS

Figure: Basic model Figure: Extended model

22

Appendix

EXTRACTION OF TOPOLOGICAL EVOLUTION

Empiricaldata

Extractsnapshots

Finaltopology

Birthtimesof nodes

Empiricalevolution

Data lacks information about time of edge creation

Assume each egde exists when both end nodes exist

We can extract the topological evolution of theempiric network.

23

Appendix

CREDITS

- Visualization of social network: LaNetVi by PolColomer-de-Simón

- Map of europe: http://en.wikipedia.org/wiki/Slovakia

- Cave painting: Patrick Gruban

24

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