The pairwise description you list correspond to a different link, namely, one where each pair is actually connected. For the shown rings, the 'correct' descript

The pairwise description you list correspond to a different link, namely, one where each pair is actually connected. For the shown rings, the 'correct' description would be: A is not connected to B B is not connected to C C is not connected to A A, B, and C are connected This seems paradoxical, but the paradox is resolved by the 'higher-order' linkage.