Driven by applications in the natural, social and computer sciences several algorithms have been proposed to enumerate all sets $X$ of vertices of a graph $G$ that induce a connected subgraph. Our algorithm AllMetricSets enumerates all $X$'s that induce (more exquisite) metric subgraphs. Here "metric" means that any distinct $s,t\in X$ are joined by a globally shortest $s-t$ path.