Name for a vertex, edge, or path that is part of a cycle

Question

I am interested in the fraction of vertices, edges, and paths that are part of a cycle in a random graph (for paths, all edges should be part of a cycle). To better search the literature, is there perhaps an established terminology for vertices, edges, or paths that are part of a cycle? So far, I found that edges that are not part of a cycle are referred to as "Bridges", or "Cut Edges", but I am looking for the inverse, and the same for vertices and paths. If there is a related concept, it might also be helpful to me.