Although every team begins the season as a member, the set isn't well-defined until every team has played at least one game. For the 2009-10 season, that didn't occur until the games of 30 November, and the initial Smith Set consisted of 138 teams.
A transitivity violation is just a set of games connected by winner→loser in which the initial winner occurs more than once in the chain. I.e. A→B→C→…→AYou can find all of the (shortest) win chains that exist in 2009 in the Second Order Winning Percentage index to the directed games graph.
The set can only become smaller as the season progresses†, and may not even exist by the end of the year. Just one week after the field became connected, there were only 44 members.
We can use this concept to make precise (or at least unambiguous) the notions of "good win", "good loss", and "bad loss." "Bad win" only has meaning in the context of specific ratings that reduce a team's value because of the losing team's rating.
"Bad losses" are especially interesting from this perspective, because when a team leaves the Smith Set so do all of the teams who were in it only because their losses were previously "good losses" (to teams in the set.) Florida's loss to Syracuse was a "good loss" because Florida remained in the set, but if Syracuse were to lose to St. Francis, Florida (along with Cal, UNC and Cornell) would drop out along with the Orange.
Tracking the Smith Set is a new report wherein I'll list the current members and upcoming games that will affect the membership status of its teams. Current members of the Smith Set are listed in italics, and the Dependent Teams column lists the teams that will drop out if the italicized team loses.