This approach allows to delete all duplicate nodes with their relationships.

START project=node(123)
MATCH project-[:T]->tA<-[:F]-jA
WITH project, MIN(ID(jA)) AS minId
MATCH project-[:T]->tB<-[:F]-jB
WHERE ID(jB)>minId
WITH jB
MATCH jB-[r]-()
DELETE jB,r

In the result we will have one single node without duplicates.

UPD. The idea was good, but it not works as desired.