Problem $5$

Imagine an academic network, where new students join the network from time to time by

connecting to their advisors. New edges are also formed between existing members who

collaborate on research. People tend to collaborate with others who have similar interests, who

are close enough to have face$-$to$-$face conversations, who have collaborated with them in the

past, and who are introduced by their past collaborators, etc. But occasionally there are also

collaborations that are quite random. Sociologists sometimes team up with computer scientists;

US professors spend sabbaticals in Europe and have collaborations there; a student goes out for

internship and thus brings together his thesis advisor and his internship mentor.

a$)$ Is it better to model the network as a directed or undirected network? Why? $(4$ points$)$

b$)$ Are we likely to observe multiple sub$-$communities in this network? Why or why not? $(4$

points$)$

c$)$ Do you expect this network to have small$-$world properties? Why or why not? $(4$ points$)$

d$)$ To visualize the edges in this network, write down two design choices that you think are the

most useful so that a viewer would be able to get a good sense of the network through the

visualization $(4$ points$)$