2. Consider the model from Chapter 19 for the spread of a new behavior through a

Question

2. Consider the model from Chapter 19 for the spread of a new behavior through a social network. Suppose we have the social network depicted in Figure 19 suppose that each node starts with the behavior B, and each node has a threshold of q for switching to behavior A. (a) 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? G ve a brief (1-2 sentence) explanation for your answer 604 CHAPTER 19. CASCADING BEHAVIOR IN NETWORKS Figure 19.27: Starting from nodes e and f, the new behavior A fails to spread to the entire graph

Explanation / Answer

aANS: As iff the other_nodes followw the threshold_rule for choosing the 'behaviors' "" {c,d,f,e,i,h} "" nodes will eventually switch to 'A'

so the answer is {c,d,f,e,i,h}

bANS: The { g,j,k } is a cluster of density " 2/3 " that is more than " 3/5 "

cANS: you can add an edge from 'd' to 'j' . Then. in this following way the threshold are met for 'j' , then 'j' can switch to behavior 'A' , and then also 'g' and 'k' can switch. Alternatively, you cann add an edge from 'c' to 'g' which will have a similar effect. Finally, the 3rd choice is to add an edge from 'c' to 'j' which might also do the task.

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