INNOVATION SPREADING:
A PROCESS ON MULTIPLE SCALES
János Kertész
Central European University
Center for Network Science
Lorentz Centre, Leiden, 2013
In collaboration with:
Márton Karsai
Northeastern University  Université de Lyon
Gerardo Iñiguez
Kimmo Kaski
Aalto University
Ando Sabbas
Skype Research Labs
Marlon Dumas
Tartu University
Outline
- Role of innovations in economy
- Innovation diffusion
- Skype data and network characteristics
- Mean field theory of spreading
- Predictions, scenarios and correlations with
global characteristics
- Summary, to do
Role of innovation in economy
Equilibrium theories: Static view. There are needs
(demand), which can be satisfied by supply of goods and
services at the price determined by their balance.
Change one parameter and assume smooth dependence.
Economic growth: Non-equilibrium. Increasing productivity,
new products, new demand. (Schumpeter’s “creative
destruction”).
Key element: Innovation
Innovation: creation of novel values through invention,
ideas, technologies, processes.
In 1898 the first international urban
planning conference convened in New
York. One topic dominated discussion:
manure. Cities all over the world,
including Sydney, were experiencing the
same problem. Unable to see any
solution to the manure crisis, the
delegates abandoned the conference after
three days instead of the scheduled ten
days.
Then, quite quickly, the crisis passed as
millions of horses were replaced by
millions of motor vehicles.
Cars were cheaper to own and operate
than horse-drawn vehicles, both for the
individual and for society. In 1900, 4,192
cars were sold in the US; by 1912 that
number had risen to 356,000. In 1912,
traffic counts in New York showed more
cars than horses for the first time.
http://bytesdaily.blogspot.nl/2011/07/great-horse-manure-crisis-of-1894.html
Invention is not enough, success is needed!
(see, e.g., typing keyboard as a counterexample)
Spreading (diffusion) of innovations
For success the innovation has to spread through the
target population. Verbal theory (E.M. Rogers)
Innovators: 2.5%
Early Adopters: 13.5%
Early majority: 34%
Late majority 34%
Laggards 16%
Adoption rate
Spreading mechanism
p: probability of adoption
m: market potential
Mahajan, Muller and Bass (1990)
Network effects are crucial
Diffusion networks
- Two effects: peer communication and mass media
- Social learning theory (“microscopic” mechanism)
- Sociological aspects (Opinion leadership, homophily
as a barrier)
- Analogies and differences to epidemic spreading
- SOCIAL NETWORK STRUCTURE, cascading on
networks
Mathematical models for (epidemic) spreading
Nodes can be in different states
Susceptible (S)  Target population for innovation: not yet adopters
Infected (I)  Adopters
Recovered (R)  Terminated
Different rates describe the transitions between these states,
depending on the microscopic details of the process. In epidemics,
if I meets S, SI, IR spontaneously, R S sometimes etc.
Accordingly, there are families of spreading models:
SI
SIR
SIRS
etc.
Huge amount of literature (e.g. Barrat, Barthelémy, Vespignani book)
Effect of the network structure on spreading
Network of social
contacts has
nontrivial mesoscale
structure: There are
strongly wired
communities connected by weak ties
“The strength of
weak ties”
Granovetter 1976
Onnela et al. PNAS, 2007
Diffusion of information
Knowledge of information diffusion based on unweighted networks
Use the empirical network to study diffusion on a weighted network:
Does the local relationship between topology and tie strength have
an effect?
Spreading simulation: infect one node with new information
(1) Empirical:
pij  wij
(2) Reference: pij  <w>
Spreading significantly faster on the reference (average weight) network
Information gets trapped in communities in the real network
SI dynamics
Reference
Empirical
Diffusion of information
Where do individuals get their information? Majority of both weak
and strong ties have subordinate role as information sources!
The importance of intermediate ties!
Empirical
Reference
Correlations influence spreading
-
Topology (community structure)
Weight-topology
Daily pattern
Bursty dynamics
Link-link dynamic correlations
Karsai et al. PRE (R) 2011
Correlations influence spreading
Event stamps based simulation
Reference systems by appropriate
shuffling.
Dominant decelerating effect
Weight-topology + burstiness
Innovation spreading in the society
Data from Skype:
Information about:
- Basic service
network
- Adoption of
additional
services
- Data about
location (IP)
Social network layer
Online social network layer
Online service network layer
unknown
Separation of time scales
Skype slides missing
Summary
• Innovations are crucial for understanding the dynamics
of the economy
• Diffusion of innovation is a mechanism with parallels
and differences to spreading of diseases
• Network correlations influence spreading speed
significantly
• Skype data are ideal to study diffusion of innovation,
which can be modeled as adoption and terminating
process
• Basic processes are: Spontaneous adoption, peer
pressure, temporal halt and terminating
• We verified that pear pressure is proportional to the rate
of adopting neighbors
• Mean field works surprisingly well
• Correlations with country characteristics
Thank you!
NOTE: Postdoc position open at CEU Center for Network Science
Contact me: janos.kertesz@gmail.com