How can I generate all labelled *connected* simple graphs on `n` vertices?

In the image below, I drew examples with number of vertices `n = 3` and `n = 4`.

For `n = 3`, there are only 4 graphs that connect all vertices.  

For `n = 4`, I only drew some as there are many more so did not draw all here.

I would like to create a function that if I input the number of vertices then it generates all graphs like the image below.

Any idea to do this?

The layout of graphs is not important but I want to label vertices's names with number or letters. Self-loop is not possible and there is only one edge between two vertices.

[![enter image description here](https://i.stack.imgur.com/NQiBk.png)](https://i.stack.imgur.com/NQiBk.png)