Apart from Tiberius, all the Julio-Claudian emperors were related to him by blood. Tiberius was the son of Tiberius Nero and Livia (from her first marriage), so there is actually no tie at all to Augustus apart from his mother being empress.

Caligula was the nephew of Claudius, who was the grandson of Livia and Tiberius Nero (above), but also of Mark Anthony and Octavia (Augustus' sister). Caligula's relation to Augustus is kinda complicated so it's I find it easier to just remember that he was the nephew of his successor. However, Caligula's mother was the daughter of Agrippa and Julia (Augustus' daughter), meaning that his ties to the first emperor are strong, but complicated. And hold on to your hat now, Nero was the son of Caligula's sister. Meaning that his ties to Augustus are through his mother's brother's grandmother - Julia.

All of these successions are made a lot more complicated than they seemingly would have to be by the Romans not having maternal succession. Livia and Augustus didn't have any children together, but they both had children from previous marriages.