Which of the following is true about communities and cascade sizes in networks with a homogenous linear threshold model (assume that the threshold is )?
1. The cascade can reach the entire network only if the linear threshold is less than the lowest community density in the network.
2. The cascade can reach the entire network only if the initial set of active nodes includes a node in each community.
3. The nodes of the network are inactive except for the initial set of active nodes. The resulting cascade cannot reach the members of a community if the density of that community is greater than .
4. The nodes of the network are inactive except for the initial set of active nodes. The resulting cascade cannot reach the members of a community if the density of that community is greater than .