3. Suppose you're working with a group of researchers studying social communication networks, with a particular focus on the distances between people in such networks, and the broader implications for the small-world phenomenon. The research group is currently negotiating an agreement with a large mobile phone carrier to get a snapshot of their "who-calls-whom" graph. Specifically, under a strict confidentiality agreement, the carrier is offering to provide a graph in which there is a node representing each of the carrier's customers, and each edge represents a pair of people who called each other over a fixed one-year period. (The edges will be annotated with the number of calls and the time at which each one happened. No personal identification will be provided with the nodes.) Recently, the carrier has proposed that instead of providing all the data, they'll only provide edges corresponding to pairs of people who called each other at least once a week on average over the course of the year. (That is, all nodes will be present, but there will only be edges for pairs of people who talked at least 52 times.) The carrier