Hello Mashiah
Connectivity is a property of a graph as a whole, there is no way to analyze it having just a part of all nodes and edges. Use of original tables in language database or use of MyISAM tables makes the analysis far too slow. Good thing with memory tables is not only in being located in memory (which is not always true of course), the engine is optimized for speed itself and the format is designed to allow that.
If your project requires more resources than are available as your fair share on the toolserver, then either the need for resources needs to be reduced, or the project has to run elsewhere. If there are good reasons and sufficient funding, setting aside a VM or even a full server for a special project can be considered. How individual projects and chapters can participate more in the givernance (and funding) of the toolserver is one of the topics that will be discussed at the upcoming chapter's conference in april in berlin. I suggest you contact someone who will attend the meeting, and discuss the issue with them.
Anyway, if using MySQL's memory tables consumes too much resources, perhaps consider alternatives? Have you looked at network analysis frameworks like JUNG (Java) or SNAP (C++)? Relational databases are not good at managing linked structures like trees and graphs anyway.
The memory requirements shouldn't be that huge anyway: two IDs per edge = 8 byte. The German language Wikipedia for instance has about 13 million links in the main namespace, 8*|E| would need about 1GB even for a naive implementation. With a little more effort, it can be nearly halved to 4*|E|+4*|V|.
I have used the trivial edge store for analyzing the category structure before, and Neil Harris is currently working on an nice standalone implementation of this for Wikimedia Germany. This should allow recursive category lookup in microseconds.
In any case, something needs to change. You can't expect to be frequently using 1/8 of the toolserver's RAM. Even more so since this amount of memory can't be used by MySQL for caching while you are not using it (because of the way the innodb cache pool works).
Regards, Daniel