Unformatted text preview: scades on Random Networks
Watts PNAS 2002
• Each node can be in one of two states, say {+1, −1}.
• Start with almost all nodes in {−1}, but just one node (or a
small fraction of nodes) in {+1}.
• Nodes update state asynchronously. For node j if the fraction
of its neighbors in state +1 is greater than a threshold function
Φj , j switches to +1 and stays in that state forever.
• The thresholds Φj are drawn at random from a distribution f (Φ)
1
which is normalized in the usual way: 0 f (Φ)dΦ = 1.
• Local dependence, fractional threshold Φj , heterogeneous
degree make this model differ from contact processes. Global cascades?
• Question: for what kinds of networks and thresholds will a
small perturbation (of even one node) cause a fraction of all
nodes to ﬂip? (i.e. a global cascade).
• Some terms:
Innovator – The ﬁrst node(s) ﬂipped to +1.
Early adopter / vulnerable – A neighbor of innovator who ﬂips
right away.
• Early adopter much have threshold Φj ...
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 Winter '11
 RaissaD'Souza
 Graph Theory

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