I am still a bit unclear but I am happy to adjust the response if more data becomes available.
Assuming that what you have now resembles a weight matrix $W$, where the weights are the transmission rates of each link, then, the total bandwidth is simply the sum of all entries of $W$.
This doesn't say much about the network.
If, instead, you were to calculate a suitable average of $W$, then that would tell you the average bandwidth between any two nodes. A better approximation to that would be an all-to-all "shortest" path calculation which would take $W$ into account.
This is a bit more informative about the network's "bandwidth" between its nodes.
Finally, you could calculate the network's throughput. This metric can take into account what is actually sent through the network and might be a more accurate, given the circumstances.
You also mention "distance". In this case, you might have to derive an average "weight" for each link for a given distance / conditions to study the bandwidth/rate/throughput behaviour at different configurations.
Hope this helps.
It has subsequently come to my attention through this question that the phrase "...the weights are the transmission rates of each link, then, the total bandwidth is simply the sum of all entries of $W$." contains an error when it practically equates bandwidth with transmission rate. This is not correct even for something as simple as BPSK. The "differences" are due to the Baud Rate and encoding schemes employed.