Generating network with random edges and then displaying edges with networkx?

I need to generate a network with 1,000 nodes and a random number of edges. I need to be able to visualize the network and see where the edges are, but don't need a weighted edge or anything like that. The edges can be connected to the nodes randomly but every node has to be connected.

I have tried using a juypter notebook and have imported matplotlib and networkx. I have been able to define or add nodes with "G.add_nodes_from([1,1000])". I am super new at this so apologies in advance if this sounds dumb.