Network Science

HW$-5(12$ points$)$

Exercise $1(2$ points$)$

Consider the fractional threshold model for the network on the left. The threshold is $\backslash (1/2\backslash )$ for all nodes.

$1.$ Suppose only one node can be chosen as an initial adopter. Which node should be chosen to obtain the largest cascade?

$2.$ Find any set of initial adopters whose activation causes the complete cascade. Exercise $2(2$ points$)$

Consider the fractional threshold model for the network on the left. Suppose all nodes have the same threshold. What is the maximum threshold such that the activation of a single initial adopter causes the complete cascade? Why?