Assassin question

Hello!
I'd like to know if an 8-player assassin game is necessarily comprised of a single chain that includes all 8 players, like
A->B->C->D->E->F->G->H->A, or if there may be more than 1 chain in the game, for instance, A>B->C->D->A and E->F->G->H->E?
In other words, if you draw a line from one player to its target and so on, do you necessarily make an octagon or can you make two separate squares (or maybe one triangle and one pentagon)?
I'd like to know if an 8-player assassin game is necessarily comprised of a single chain that includes all 8 players, like
A->B->C->D->E->F->G->H->A, or if there may be more than 1 chain in the game, for instance, A>B->C->D->A and E->F->G->H->E?
In other words, if you draw a line from one player to its target and so on, do you necessarily make an octagon or can you make two separate squares (or maybe one triangle and one pentagon)?