DCS/CSCI 2350 Social & Economic Networks How do diseases, - - PDF document
10/29/20 DCS/CSCI 2350 Social & Economic Networks How do diseases, behavior, opinion, technology, etc. propagate in a network? Cascading Behavior in Networks Reading: Ch 19 of EK Mohammad T . Irfan Diffusion of innovations u
u Studied in sociology since 1940s u One’s choice influences others u Indirect/informational effects – social
u Photo/video going viral
u Direct-benefit effects
u Technology adoption– Xbox/PS4, phone, fax,
email, FB
u Adoption of hybrid seed corn in Iowa
u Ryan and Gross, 1943
u Adoption of tetracycline by US doctors
u Coleman, Katz, and Menzel, 1966
u Shared ingredients
u Indirect effects u Adoption was high-risk, high-gain u Early adopters had higher socioeconomic status u Social structure was important– visibility of
neighbors’ activity
u Complexity u Observability u Trialability u Compatibility
u Modeling diffusion u Connection with the things we know
u Homophily u Clustering u The strength of weak ties
u Mark Granovetter's threshold model of
u Side note: collective behavior vs. collective action
u Model: An individual will adopt action A if at
u Example
u Emergence of a riot in a crowd of 100 people
(complete graph)
u Thresholds of individuals to get violent
u 0, 1, 2, ..., 99
u What will happen?
u Extensions
u General network u Distribution of thresholds
u Difference with Schelling's model: In Granovetter's
model, slight change of thresholds may lead to completely different global outcome. Extremely important that someone has a threshold
u Explicitly model direct-benefit effect
u "Networked coordination game"
u Model
u 2 choices– A (Slack) and B (Skype) u “Payoffs” of any two friends v & w in a network u Payoffs are interdependent u Each individual wants to get the maximum possible
payoff subject to what others are doing
u What action will v adopt (A or B)?
p fraction of v's friends: A (1-p) fraction: B Degree of v = d v will adopt A if: p >= b/(a+b) Threshold, q = b/(a+b) for switching from B to A
u Facilitates diffusion u Granovetter's model: the persons with
u Modeling assumption by Kleinberg & many others
u Initially everyone does B u Payoff parameters: b = 2, a = 3 u Threshold for switching from B to A, q = 2/5 u We will set two initial adopters of A and "play
u Def. A set of initial adopters causes a
u Always happens?
u Initial adopters u Network structure u Threshold value q
u Quality of product– payoff parameters a and b
u Example: viral marketing
u Weak ties are conveyors of information u But cannot “force” adoption of behavior
Would Align with own community
u Does clustering help diffusion?
Every node in these clusters have at most 1/3 fraction
Will they ever adopt the new behavior?
u Assuming a threshold of q, cascade will be
u Cluster density: minimum over the nodes in a cluster
{fraction of neighbors of the node that belong to the same cluster}
density = 2/3 > 1-q for q = 2/5
u Node v’s threshold = bv/(av + bv)
u Same calculation as before
u All friendships are not the same!
u Thresholds are heterogeneous u Directed, asymmetric network u Relationships can be positive or negative
u Switching back and forth two actions are allowed
u Initial adopters or seed nodes
Granovetter: seeds must have threshold 0 Kleinberg: seeds can be externally set (their thresholds don't matter) What can go wrong? We: seeds can be externally set as long as their threshold requirements are fulfilled at the end of diffusion