How many roads are there out of an individual city?
Maybe there's 20 rows out of an individual city, that might even be a big city.
So a density of 0.1 on a big map
is not all that, this would mean,
0.1 would mean that on average,
we're going to get 5,000 edges
per node. Here it was an average one half edge
per node.
When half edge per node for a small graph, it's going to leave us unconnected.
5,000 edges out of a 50,000 node graph is
going to leave us with a humongous number of paths
in that graph and it's very likely that, almost
certainly, with probability approaching 1, going to be connected.
So if you have a good intuition, about what we've been talking
about with these randomly generated graphs and this is going to come up
in the homework I'm assigning you, as the graphs get larger, namely
the number of vertices, the number of nodes in the graphs get larger.
Having a particular density makes it more and more
likely that there are paths between all the nodes.