In your introductory referee class, you learned that the referee would run on a diagonal line so they can keep the play between themselves and an assistant referee. While this statement is true, the referee should not run on a diagonal "line." Their diagonal must be much wider than a line.
When a play goes to a referee quadrant, no assistant referee is close. Therefore, the referee needs to get closer to the play by going wider to their left on their diagonal line. When a play goes closer to the assistant referee, the referee still needs to increase their presence because the assistant referee frequently has to worry about offside or the ball in-and-out. This means that the referee must go wider to their right on their diagonal.
Furthermore, by having a wider diagonal, the referee is able to have a better view of an incident that could happen on the field. In the video below, the referee remains central on the field without width. As a result, when an offense occurs, he does not have good proximity. A few players are between the referee and the challenge. In addition, he is not in the best position to judge the direction of play, which is one of the criterial to decide if an offense is a denial of an obvious goal scoring opportunity.