How long does it take for a transaction to propagate over the network?

This is not something a node can do on its own. To calculate the propagation time estimate, multiple active monitoring nodes (modification/running custom software) must be deployed.

This is the approach that follows, as far as I know, kit@dsn. They collect and report multiple statistics on their website, including transaction propagation times.

According to the latest data, it takes about 7 seconds to reach 50% of the network, about 17 seconds, and reaches 90%. Note that this does not mean it takes too long to reach the miner. Miners are more likely to be connected better than regular nodes, so they expect to receive most transactions close to the 7-second mark.