Unformatted text preview: the social
sciences (Peyton Young, Granovetter, Martin Nowak ...;
diffusion of innovation; societal norms)
• Recent theorems: “network coordination games” (bigger
payout if connected nodes in the same state)
(Kleinberg, Kempe, Tardos, Dodds, Watts, Domingos)
• Finding the inﬂuential set of nodes, or the k most inﬂuential
Often NP-hard and not amenable to approximation algorithms
• Key distinction:
– thresholds of activation (leads to unpredictable behaviors)
– diminishing returns (submodular functions nicer) Diffusion, Cascade behaviors, and inﬂuential nodes
Part III: Markov chains and mixing times
• New game-theoretic approaches (general coordination games)
– Results in an Ising model.
– Montanari and Saberi PNAS 2010.
• Techniques from Parts I and II suggest:
– Innovations spread quickly in highly connected networks.
– Long-range links beneﬁt spreading.
– High-degree nodes quite inﬂuential (enhance spreading).
• Techniques from Part III suggest:
– Innovations spread quickly in locally connec...
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- Winter '11
- Graph Theory