So, we find out in The Son of Neptune that Frank is related to Periclymenus, a son of Poseidon. Percy is also a son of Poseidon linking the two.
We also learn that Hazel knew a boy named Sammy when she was younger back in the 1930-40's who may be related to Leo as the two look exactly alike. That connects Hazel and Leo.
Piper was also good friends with Leo before she knew they were demigods so that connects Piper, Leo, and Hazel.
Hazel likes Frank and if they are a couple now, that connects Piper, Leo, Hazel, Frank, and Percy.
If Annabeth is one of the seven, she is dating Percy connecting her to the rest of them.
Lastly, Jason is Thalia's brother, and Thalia is friends with Percy and Annabeth connecting them all together.
So their may be more connections in later books as some of these connections are kind of vague, but there are no coincidences. What other connections bring together these characters?