Discriminate closed-chain from open-chain

I have two classes of chains: closed-chains where a random path ends near where it starts (ie. loop), and open-chains without this restriction (ie. random walk). These chains are a directed graph connecting discrete points ($x, y, z)$ (ie. $n$ points, $n-1$ vectors) with sequential order.

One way I have tried to discriminate these two chains is by analyzing the start-end distances. Expectedly, the start-end distance of closed-chains is small, while the start-end distance of open-chains is large. There is a noticeable overlap that will result in false-positives/false-negatives.

What are some other metrics one might discriminate these two types of chains? I thought perhaps angular momentum might be useful, but it is unclear how to derive a metric more robust than this start-end distance.