You could use "recursion": have one turtle ask its link-neighbors to execute some code that includes asking their link-neighbors to execute the same code.
ask one-of turtles [ move-neighbors ]
to move-neighbors
fd 1 ; or whatever you want all the linked turtles to do
ask link-neighbors [ move-neighbors ]
end
But I think you will be happier if you learn to use the built-in Networks extension. It has commands for doing things like this.
Steve R.