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Information Diffusion - Complex Networks - Lecture Slides, Slides of Data Communication Systems and Computer Networks

During the course of the Complex Networks, we study the different concept regarding the complex computer networking. The main points upon which in these lecture slides focused are:Information Diffusion, Factors Influencing, Strength of Ties, Network Structure, Connected, Granovetter, Onnela, Kossinets, Interlocks, Adoption of Practices

Typology: Slides

2012/2013

Uploaded on 04/23/2013

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Lecture 19:
Information diffusion in networks
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Lecture 19:

Information diffusion in networks

outline

 factors influencing information diffusion

 network structure: which nodes are connected?  strength of ties: how strong are the connections?

 studies in information diffusion:

 Granovetter: the strength of weak ties  J-P Onnela et al: strength of intermediate ties  Kossinets et al: strength of backbone ties  Davis: board interlocks and adoption of practices

 network position and access to information

 Burt: Structural holes and good ideas  Aral and van Alstyne: networks and information advantage

 networks and innovation

 Lazer and Friedman: innovation

Strong tie defined

 A strong tie

 frequent contact  affinity  many mutual contacts

 Less likely to be a bridge (or a local bridge)

“forbidden triad”: strong ties are likely to “close”

Source: Granovetter, M. (1973). "The Strength of Weak Ties",

school kids and 1st^ through 8th^ choices of friends

 snowball sampling:

 will you reach more different kids by asking each kid to name their 2 best friends, or their 7 th^ & 8 th^ closest friend?

Source: M. van Alstyne, S. Aral. Networks, Information & Social Capital Docsity.com

how does strength of a tie influence diffusion?

 M. S. Granovetter: The Strength of Weak Ties , AJS, 1973:

 finding a job through a contact that one saw

 frequently (2+ times/week) 16.7%  occasionally (more than once a year but < 2x week) 55.6%  rarely 27.8%

 but… length of path is short

 contact directly works for/is the employer  or is connected directly to employer

strength of tie: frequency of communication

 Kossinets, Watts, Kleinberg, KDD 2008:

 which paths yield the most up to date info?  how many of the edges form the “backbone”?

source: Kossinets et al. “The structure of information pathways in a social communication network”Docsity.com

source: Onnela J. et.al. Structure and tie strengths in mobile communication networks

Localized strong ties slow infection spread.

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how can information diffusion be different from

simple contagion (e.g. a virus)?

 simple contagion:

 infected individual infects neighbors with information at some rate

 threshold contagion:

 individuals must hear information (or observe behavior) from a number or fraction of friends before adopting

 in lab: complex contagion (Centola & Macy, AJS, 2007)

 how do you pick individuals to “infect” such that your opinion prevails

http://projects.si.umich.edu/netlearn/NetLogo4/DiffusionCompetition.html

Framework (Continued)

 Homogeneous birth rate β on all edges between infected

and susceptible nodes

 Homogeneous death rate δ for infected nodes

Infected

Healthy

N1 X
N
N

Prob. β

Prob. δ

SIR and SIS Models

An SIR model consists of three group

 Susceptible: Those who may contract the disease  Infected: Those infected  Recovered: Those with natural immunity or those that have died.

An SIS model consists of two group

 Susceptible: Those who may contract the disease  Infected: Those infected

SIR and SIS Models

SIR Model:

SIS Model:

R I

I SI I

S SI

I SI I

S SI I

Threshold dynamics

The network:

  • a (^) ij is the adjacency matrix (N ×N)
  • un-weighted
  • undirected

The nodes:

  • are labelled i , i from 1 to N;
  • have a state ;
  • and a threshold ri from some distribution.

aij ∈ {0,1}

aij = a ji

vi ( t )∈{ 0 , 1 }

diffusion of innovation

 surveys:

 farmers adopting new varieties of hybrid corn by observing what their neighbors were planting (Ryan and Gross, 1943)  doctors prescribing new medication (Coleman et al. 1957)  spread of obesity & happiness in social networks (Christakis and Fowler, 2008)

 online behavioral data:  Spread of Flickr photos & Digg stories (Lerman, 2007)  joining LiveJournal groups & CS conferences (Backstrom et al. 2006)  + others e.g. Anagnostopoulos et al. 2008

20

Open question: how do we tell influence from

correlation?

 approaches:

 time resolved data: if adoption time is shuffled, does it yield the same patterns?  if edges are directed: does reversing the edge direction yield less predictive power?