Q:

Formal name for a closed connected graph

I have to name an abstraction representing a mechanical truss diagram. It consists of a set of polygons that must  overlap, viz. share an edge or a corner. In other words it must not only be a connected graph but it must also form a closed shape. Is there an existing term that describes this?

A:

The 'shape' of the graph is not so important - where the lines lie in two-space is merely an abstraction for visual convenience. It is, in a sense, arbitrary.
However, it is possible that you are referring to a graph composed of several cycles. A cyclic graph is a graph that forms a 'closed shape' because it forms a closed walk, and it seems possible to me that you are referring to a connected graph in which every vertex is in a cyclic subgraph: if every vertex is in a cyclic subgraph, then your 'shape' will necessarily be 'closed', as there will be no vertices with only one edge.
I don't think there's a technical term for that, but the italicized description should do.

