1. Consider the decision model/game theoretic model from Chapter 19 for the spread of a new behavior through a social network. Suppose we have the social network depicted in Figure 2; suppose that each node starts with the behavior B, and each node has a threshold of q = 2/5 for switching to behavior A.
   1. Now, let c 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? Give a brief explanation for your answer.
   2. Find a cluster of density greater than 1 ? q = 3/5 in the part of the graph outside S that blocks behavior A from spreading to all nodes, starting from S, at threshold q. Give a brief explanation for your answer.
   3. Suppose you were allowed to add a single edge to the given network, connecting one of nodes c or d to any one node that it is not currently connected to. Could make this in such a way that now behavior A, starting from S and spreading with a threshold of 2/5, would reach all nodes? Give a brief explanation for your answer.

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