The plot of this brilliant play can be considered to be complex because of the very curious and almost unique way in which the play is constructed. Many critics over the years have argued that what makes the play's plot so complex is the way that it is a kind of detective hunt, as Oedipus tries to find the murderer of his father, only to discover that the search for the killer points more and more towards himself. He is the killer that he pledges to find at the beginning of the play and this pledge comes with tremendous irony:

I will speak out now as a stranger to the story,
a stranger to the crime. If I'd been present then,
there would have been no mystery, no long hunt
without a clue in hand.

The dramatic irony of the play is another factor that could be argued to give it a complex plot. Almost every line contains some form of dramatic irony, as we watch the play move towards its inevitable conclusion and Oedipus achieves tragic self-knowledge about who he is.