The document discusses complex systems and networks, focusing on digital networks. It describes how network models can help understand complex systems like the internet and financial networks. Digital networks have significant power to influence behaviors and spread information. While this power in a single network could be problematic, models show how diversity across multiple competing networks can allow for coexistence, though this is fragile. Sustaining diversity requires balancing viral and mass media influences.

1. (Digital) networks and
the science of complex systems
Kaj Kolja Kleineberg | kkleineberg@ethz.ch
@KoljaKleineberg | koljakleineberg.wordpress.com

2. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Agenda:
From complex systems to digital networks
1. Networks and complex systems
2. The power of digital networks
3. Sustaining digital diversity
4. Summary
2

3. NETWORKS AND COMPLEX SYSTEMS

4. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
A chess riddle:
Swap the positions of the black and white knights
4Credits: Marian Boguna

5. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
A chess riddle:
Network approach makes the problem really easy
5Credits: Marian Boguna

6. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
A chess riddle:
Network approach makes the problem really easy
5Credits: Marian Boguna

7. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
A chess riddle:
Network approach makes the problem really easy
5Credits: Marian Boguna

8. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
A chess riddle:
Network approach makes the problem really easy
5Credits: Marian Boguna

9. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
A chess riddle:
Network approach makes the problem really easy
5Credits: Marian Boguna

10. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Seven bridges of Königsberg:
crossing each bridge only once
The city of Königsberg was set on both sides of the Pregel River,
and included two large islands which were connected to each
other, or to the two mainland portions of the city, by seven
bridges. The problem was to devise a walk through the city that
would cross each of those bridges once and only once.
6

11. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Seven bridges of Königsberg:
the foundation of graph theory
https://en.wikipedia.org/wiki/Seven_Bridges_of_Königsberg
Is it possible to cross all bridges only once?
7

12. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Seven bridges of Königsberg:
the foundation of graph theory
https://en.wikipedia.org/wiki/Seven_Bridges_of_Königsberg
Is it possible to cross all bridges only once?
Whenever one enters a node by a bridge, one leaves the node by a bridge
The number of times one enters a non-terminal node equals the number of
times one leaves it → even number except for start endpoint
However, all nodes have uneven number of bridges attached →
Contradiction
7

13. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
complex networks
8

14. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
complex networks
Complex networks are maps of complex
systems.
8

15. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
What is a complex system?
9

16. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Definition:
What is a complex system?
...the whole is more than the sum of the parts, [...] in
the sense that, given the properties of the parts and the
laws of their interaction, it is not a trivial matter to infer
the properties of the whole.
Herbert A. Simon
10

17. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Definition:
What is a complex system?
...the whole is more than the sum of the parts, [...] in
the sense that, given the properties of the parts and the
laws of their interaction, it is not a trivial matter to infer
the properties of the whole.
Herbert A. Simon
Large number
of components
10

18. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Definition:
What is a complex system?
...the whole is more than the sum of the parts, [...] in
the sense that, given the properties of the parts and the
laws of their interaction, it is not a trivial matter to infer
the properties of the whole.
Herbert A. Simon
Large number
of components
Nonlinear
interactions
10

19. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Definition:
What is a complex system?
...the whole is more than the sum of the parts, [...] in
the sense that, given the properties of the parts and the
laws of their interaction, it is not a trivial matter to infer
the properties of the whole.
Herbert A. Simon
Large number
of components
Nonlinear
interactions
Emergent
behavior
10

20. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
A car is not a complex system
(we call it a difficult system)
11

21. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
The Internet is a complex system
(without a central masterplan)
12

22. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
The Internet is a complex system:
lack of scale
13Nature, 401:130-131 (1999)

23. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Scale-free property common to many real complex networks
induces a vanishing epidemic threshold
14

24. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Networks allow us to map interactions
and study system-level implications
15Nature Physics 10, 762-767 (2014); Phys. Rev. Lett. 109, 064101 (2013)

25. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Financial networks
and systemic risk (debt rank)
16

26. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Similar procedure allows Google
to rank websites (page rank)
17

27. THE POWER OF DIGITAL NETWORKS

28. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Facebook likes predict your personality
better than your spouse
19

29. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Social messages can influence
real world voting behavior
20

30. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Search algorithms can also change
real world voting behavior
21

31. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Algorithms can change how you feel
by changing your Facebook timeline
22

32. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
What if all this power
is in one hand?
23

33. SUSTAINING DIGITAL DIVERSITY

34. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Model contains spreading dynamics
and the influence of mass media
Online social
network layer
Traditional contact
network layer
Active
Online offline
Passive
Online offline
Susceptible
Only offline
25

35. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Model contains spreading dynamics
and the influence of mass media
Online social
network layer
Traditional contact
network layer
Active
Online offline
Passive
Online offline
Susceptible
Only offline
Mass media activation Viral activation
Deactivation Viral reactivation
25

37. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
The evolution of isolated online social networks:
insights from a system-level description
Underlying social structure
determines topological
evolution
PRX 4, 031046, 2014
27

38. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
The evolution of isolated online social networks:
insights from a system-level description
Underlying social structure
determines topological
evolution
Balance
of viral and mass media
influence
PRX 4, 031046, 2014
27

39. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
The evolution of isolated online social networks:
insights from a system-level description
Underlying social structure
determines topological
evolution
Balance
of viral and mass media
influence
Survival and death
of networks
PRX 4, 031046, 2014
27

40. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
The evolution of isolated online social networks:
insights from a system-level description
Underlying social structure
determines topological
evolution
Balance
of viral and mass media
influence
Survival and death
of networks
Weak ties
have higher transmissibility
PRX 4, 031046, 2014
27

41. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Digital ecosystem is formed by multiple networks
competing for the attention of individuals
OSN 2
OSN 1
Underl.
network
Active
Passive
Susceptible
Partial
states}
Virality share
distribution
between OSNs
λi = ωi(ρa)λ
Rich-get-richer
more active
networks obtain
higher share
Here: ωi = [ρa
i ]σ/
∑
j[ρa
j]σ
σ: activity affinity
28Sci. Rep. 5, 10268 (2015)

42. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Coexistence (diversity) is possible but fragile:
once lost, it cannot be recovered
Stable
Unstable
0.50 0.75 1.00 1.25 1.50
0.00
0.25
0.50
0.75
0.00
0.25
0.50
0.75
Bifurcation diagram
σ
ρ1,2
a
29Sci. Rep. 5, 10268 (2015)

43. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Coexistence (diversity) is possible but fragile:
once lost, it cannot be recovered
Stable
Unstable
0.50 0.75 1.00 1.25 1.50
0.00
0.25
0.50
0.75
0.00
0.25
0.50
0.75
Bifurcation diagram
σ
ρ1,2
a
Coexistence
despite rich-get-richer
29Sci. Rep. 5, 10268 (2015)

44. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Coexistence (diversity) is possible but fragile:
once lost, it cannot be recovered
Stable
Unstable
0.50 0.75 1.00 1.25 1.50
0.00
0.25
0.50
0.75
0.00
0.25
0.50
0.75
Bifurcation diagram
σ
ρ1,2
a
Coexistence
despite rich-get-richer
Digital diversity
is irreversible
29Sci. Rep. 5, 10268 (2015)

45. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Network of multi-layer networks
represents global digital ecology
Active
Passive
Susceptible
Partial
states}
Local
network
Global
network
Effective activity
30

47. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Digital networks can coexist
but coexistence is fragile
Coexistence
despite rich-get-richer
Sci. Rep. 5, 10268 (2015) • Sci. Rep. 6, 25116 (2016)
32

48. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Digital networks can coexist
but coexistence is fragile
Coexistence
despite rich-get-richer
Diversity
is fragile
Sci. Rep. 5, 10268 (2015) • Sci. Rep. 6, 25116 (2016)
32

49. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Digital networks can coexist
but coexistence is fragile
Coexistence
despite rich-get-richer
Diversity
is fragile
Moderate
digital diversity observed
Sci. Rep. 5, 10268 (2015) • Sci. Rep. 6, 25116 (2016)
32

50. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Digital networks can coexist
but coexistence is fragile
Coexistence
despite rich-get-richer
Diversity
is fragile
Moderate
digital diversity observed
Facebook
takes over local networks
Sci. Rep. 5, 10268 (2015) • Sci. Rep. 6, 25116 (2016)
32

51. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Utility of networks: bottom-up search and navigation
with incentives based on sharing generated value
Navigation
is common function
networks perform
33Nature Communications 1, 62 (2010) • Scientific Reports 7, 2897 (2017)

52. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Utility of networks: bottom-up search and navigation
with incentives based on sharing generated value
Navigation
is common function
networks perform
Individuals
perform routing
instead of service
providers
33Nature Communications 1, 62 (2010) • Scientific Reports 7, 2897 (2017)

53. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Utility of networks: bottom-up search and navigation
with incentives based on sharing generated value
Navigation
is common function
networks perform
Individuals
perform routing
instead of service
providers
Payoff
for successful
deliveries
33Nature Communications 1, 62 (2010) • Scientific Reports 7, 2897 (2017)

55. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Navigation works better with
more active networks
35Nature Physics 12, 1076–1081 (2016)

56. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
Appropriate incentives could create a feedback loop
building on self-organization of complex systems
Qualified Money
t
o
route
activein
m
any networks
Optim
izes strategy:
Inc
entive
Sustains
digital dive
rsity
Increasesro
uting
perform
a
nce
Exchangeable
Social Bitcoin
+Reputation
Feedback loop
can overcome fragility
Digital diversity
can become robust
sustainable
36Eur. Phys. J. Spec. Top. 225: 3231 (2016)

57. SUMMARY

58. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
(Digital) networks
and the science of complex systems
Complex systems:
emergent behavior, no central
control
38

59. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
(Digital) networks
and the science of complex systems
Complex systems:
emergent behavior, no central
control
Networks
are system level maps of
interactions
38

60. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
(Digital) networks
and the science of complex systems
Complex systems:
emergent behavior, no central
control
Networks
are system level maps of
interactions
Digital networks
are extremely powerful
38

61. Networks and complex systems The power of digital networks Sustaining digital diversity Summary
(Digital) networks
and the science of complex systems
Complex systems:
emergent behavior, no central
control
Networks
are system level maps of
interactions
Digital networks
are extremely powerful
Digital diversity
could be sustained with
incentives
38

62. Kaj Kolja Kleineberg:
• kkleineberg@ethz.ch
• @KoljaKleineberg
• koljakleineberg.wordpress.com
ETH Zurich:
• Computational Social Science Group
• http://www.coss.ethz.ch

63. Kaj Kolja Kleineberg:
• kkleineberg@ethz.ch
• @KoljaKleineberg ← Slides updates
• koljakleineberg.wordpress.com
ETH Zurich:
• Computational Social Science Group
• http://www.coss.ethz.ch

64. Kaj Kolja Kleineberg:
• kkleineberg@ethz.ch
• @KoljaKleineberg ← Slides updates
• koljakleineberg.wordpress.com ← References
ETH Zurich:
• Computational Social Science Group
• http://www.coss.ethz.ch