Sender Recipients Carla, Ehaz Carla, Dana Ehaz Ann Bert Carla Dana Ann, Carla Ehaz Bert
Five people are all connected by e-mail Whenever any one of them hears a juicy piece of gossip he or she passes it along by e-mailing it to someone else in the group according to Table (a) Draw the digraph that models this "gossip network" and find its adjacency matrix A (b) Define a step as the time it takes a person to e-mail everyone on his or her list. (Thus, in one step, gossip gets from Ann to both Carla and Ehaz.) If Bert hears a rumor, how many steps will it take for everyone else to hear the rumor? What matrix calculation reveals this? (c) If Ann hears a rumor, how many steps will it take for everyone else to hear the rumor? What matrix calculation reveals this? (d) In general, if A is the adjacency matrix of a digraph, how can we tell if vertex i is connected to vertex j by a path (of some length)?
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