Problem 475. Is this group simply connected?

Given connectivity information about a graph, your job is to figure out if the graph is fully connected. You are given a list of vertex pairs that specify undirected connectivity (edges) among vertices. Vertex labels are always positive integers.

Example 1:

 Input  node_pairs = [ 8 9
                       8 3 ]
 Output tf is true

The three nodes of this graph are fully connected, since this graph could be drawn like so:

 3--8--9

Example 2:

 Input  node_pairs = [ 1 2 
                       2 3
                       1 4
                       3 4
                       5 6 ]
 Output tf is false

This graph could be drawn like so:

 1--2  5--6
 |  |
 4--3

There are two distinct subgraphs.