Ni! Hi Nikhrao,
Please note that the phrase you've extracted contains the words «during compilation» while you seem to be talking about runtime memory usage.
Runtime memory usage will depend on the algorithm you'll be running and choices of the implementation, as there's often a tradeoff between memory usage and speed.
You can count that graph-tool strikes a good balance that will serve most scenarios, and in some cases there are parameters to adjust for extreme situations. Having never used igraph, I'd assume it strives for a similar goal.
I strongly recommend you to try it yourself on your actual use case. Otherwise, you'd have to provide much more detail about it for us to give you a theoretical answer that won't be worth as much as simply running the algorithm you want on the kind of data you expect to treat.
Now, if you just want a "general idea" about memory consumption, I personally see no technical reason to expect big differences when comparing algorithms supported by both libraries.
Best,
ale
.~´