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

Docsity.com

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?