Hunter, as far as I'm aware, the nodemap was never meant to represent real-world distance from each other; it simply displays the inter-system connections in an easy-to-read format. Considering the fact that the vast majority of systems in FS1/2 are actual stars, I would expect that their real-world distances from Sol apply in-universe, as well.
Regarding the original question, that's always been one of the great mysteries of FS2, and there have been plenty of theories on the subject. One is that there's some sort of interstellar dust cloud, or other type of disturbance, located between Sol and Alpha Centauri that would prevent radio transmissions from getting through. Another is that, considering the fact that a three-year lag time would make any messages sent almost instantly out-of-date, Sol might have decided to just not bother sending them out. A rather sinister possibility is that GTVA command has received messages from Sol, but the content of them was too disturbing to be unclassified. There's also the chance that the Shivans managed to find another way into Sol, meaning that there wouldn't be anyone to send any messages. In any case, it's not something we'll likely ever know for certain.