Consider a graph of any reasonable size. Node v’s neighbors can be split into two sets: Set A contains v's neighbors who have adopted a new behavior and B is the set of those behaving conservatively. Node v will only adopt the behavior of those in A if at least a ''q'' fraction of neighbors follow behavior A.
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* if ''q'' is small, the behavior is easily adopted and easily spread
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* if ''q'' is large, B is an attractive behavior and it takes more friends to engage in A before v will switch.
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; Cascading – diffusion over the entire network
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: Consider a set of initial adopters who start with a new behavior A, while every other node starts with behavior B. Nodes then repeatedly evaluate the decision to switch from B to A using a threshold of ''q''. If the resulting cascade of adoptions of A eventually causes every node to switch from B to A, then we say that the set of initial adopters causes a complete cascade at threshold ''q''. Clusters of density ''d'' > 1 − ''q'' are obstacles to cascades across the entire network.