The above chart shows the primary successors of the apostles. These are the ones we know of through their writings.

Irenaeus says he was a disciple of Ploycarp when he was young in Against Heresies 3.3
Hippolytus, who was a disciple of Irenaeus, says Tatian was a disciple of Justin Martyr in Refutation of all Heresies 8.9