Kleinberg Chapter 19

1) 1)Consider the network depicted in Figure 19.27; suppose that each node starts with the behavior B, and each node has a threshold of q = 1/2 for switching to behavior A. (a) Now, let e and f 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? (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.

9 Figure 19.27: Starting from nodes e and f, the new behavior A fails to spread to the entire graph