Is a subgraph of G always connected I am trying to figure out if given a connect graph with N nodes and A edges, its subgraphs are connected.

In order word: given a graph G, can I have a subgraph of G that is not connected?
Or: can a subpgraph of G not be connected?

I think the answer is no because otherwise G' is not a (sub)graph.
A subgraph of a graph&nbsp;$G$ is any graph that has a subset of $G$'s vertices and a subset of its edges.  In particular, for an graph $G=(V,E)$, the graph $(V,\emptyset)$ is a subgraph that's not connected.