Question

3. Consider the network depicted below; suppose that each node starts with the
behavior B, and each node has a threshold of g = 1/2 for switching to behavior A.
(a) Now, let b and d form a two-node set S of initial adopters of behavior A. If
other nodes follow the threshold rule for choosing behaviors, which nodes will
eventually switch to A? (15pts)
(b) Find a cluster of density greater than 1- q = 1/2 in the part of the graph
outside S that blocks behavior A from spreading to all nodes, starting from S, at
threshold q. (10pts)
(c) Suppose you were allowed to add a single edge to the given network,
connecting one of nodes to any one node that it is not currently connected to. Could
you do this in such a way that now behavior A, starting from S and spreading with a
threshold of 1/2, would reach all nodes? Give a brief explanation for your answer.
(10pts)​

Answer 1

Answer:

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