The document discusses catastrophic instabilities that can occur in interacting networks and possible remedies. It summarizes research showing that coexistence among competing online social networks is possible but fragile. It proposes that providing incentives for users to route information across multiple networks could help sustain digital diversity. The document also examines how hidden geometric correlations in real-world multiplex networks can mitigate vulnerabilities to failures or attacks.

1. Catastrophic instabilities in interacting networks
and possible remedies
Kaj Kolja Kleineberg | kkleineberg@ethz.ch
@KoljaKleineberg | koljakleineberg.wordpress.com
Re-inventing Society
in the Digital Age

2. The World Economic Forum
Risks Interconnec�on Map

3. Nature 497, 51–59 (2013)

4. with incentives
Sustaining
digital diversity

5. Coexistence among competing online social networks
is possible but fragile
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
Evolution of isolated networks Multiple networks compete for attention
OSN 2
OSN 1
Underl.
network
Active
Passive
Susceptible
Partial
states}
Distribution of attention
following rich-get-richer
: activity affinity (strength
of rich-get-richer)
Coexistence is possible but fragile How many networks can coexist
Physical Review X (4) 031046 (2014) & Sci. Rep. 5, 10268 (2015)

6. Scalable navigation using latent geometric spaces
performs better with more network layers
Latent geometry
Hyperbolic spaces:
Popularity (radial)
Similarity (angular)
Efficient navigation
(greedy routing)
Credit: Marian Boguna
Multiple networks increase
navigation performance*
*: only if the layers of the multiplex exhibit "geometric correlations",
which is the case in most real multiplexes (more later)
Nature Physics 12, 1076–1081 (2016)
Kleineberg et al.
Nature Communications 1, 62 (2010)
Boguna el al.
Phys. Rev. E 82, 036106 (2010)
D. Krioukov el al.

7. Appropriate incentives to route information could
sustain digital diversity
Feedback mechanism
Assumption: Incentives to use
less active networks
navigation incentive
rich-get-richer
Qualified Money
t
o
route
ac�vein
m
any networks
Op�m
izes strategy:
Inc
en�ve
Sustains
digital dive
rsity
Increases ro
u�ng
perform
a
nce
Exchangeable
Social Bitcoin
+Reputa�on
Robustness of digital diversity
Eur. Phys. J. Spec. Top. 225: 3231 (2016), K. Kleineberg and D. Helbing

8. Interdependent systems
Robustness of
interdependent
networks

9. The World Economic Forum
Risks Interconnec�on Map

11. Extreme vulnerability of multiplex networks
can be mitigated by hidden geometric correlations
Multiplex networksLatent geometry
Hyperbolic spaces:
Popularity (radial)
Similarity (angular)
Geometric correlations
Random failures
(mutual percolation)
Targeted attacks
(remove hubs)
Geometric correlations
exist in real multiplexes
New Journal of Physics 17, 053033 (2015) & Nature Physics 12, 1076–1081 (2016) & arXiv:1702.02246

12. Catastrophic instabilities in interacting networks
and possible remedies
References:
Evolution of the Digital Society reveals Balance between Mass
Media and Viral Influence
Physical Review X (4) 031046 (2014), K. Kleineberg and M. Boguñá.
Digital Ecology: Coexistence and Domination among Interacting Networks
Sci. Rep. 5, 10268 (2015), K. Kleineberg and M. Boguñá.
Hidden geometric correlations in real multiplex networks,
Nature Physics 12, 1076–1081 (2016), K. Kleineberg et al.
A “Social Bitcoin” could sustain a democratic digital world,
Eur. Phys. J. Spec. Top. 225: 3231 (2016), K. Kleineberg and D. Helbing.
Collective navigation of complex networks: Participatory greedy routing,
arXiv:1611.04395 (accepted in Sci. Rep.), K. Kleineberg and D. Helbing.
Geometric correlations mitigate the extreme vulnerability of multiplex
networks against targeted attacks,
arXiv:1702.02246 (accepted in PRL), K. Kleineberg et al. Re-inventing Society
in the Digital Age
Contact:
kkleineberg@ethz.ch
@KoljaKleineberg
koljakleineberg.wordpress.com

13. Catastrophic instabilities in interacting networks
and possible remedies
References:
Evolution of the Digital Society reveals Balance between Mass
Media and Viral Influence
Physical Review X (4) 031046 (2014), K. Kleineberg and M. Boguñá.
Digital Ecology: Coexistence and Domination among Interacting Networks
Sci. Rep. 5, 10268 (2015), K. Kleineberg and M. Boguñá.
Hidden geometric correlations in real multiplex networks,
Nature Physics 12, 1076–1081 (2016), K. Kleineberg et al.
A “Social Bitcoin” could sustain a democratic digital world,
Eur. Phys. J. Spec. Top. 225: 3231 (2016), K. Kleineberg and D. Helbing.
Collective navigation of complex networks: Participatory greedy routing,
arXiv:1611.04395 (accepted in Sci. Rep.), K. Kleineberg and D. Helbing.
Geometric correlations mitigate the extreme vulnerability of multiplex
networks against targeted attacks,
arXiv:1702.02246 (accepted in PRL), K. Kleineberg et al. Re-inventing Society
in the Digital Age
Contact:
kkleineberg@ethz.ch
@KoljaKleineberg
koljakleineberg.wordpress.com
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