
My first thought as a way to deal with this, was to make it so ‘Other’ and ‘Character’ relations would not propagate when they were graphed. That means that if A has an 'other' relation to B and B has relations to C and D, if you looked at the graph of A it would only have A and B (and not the things related to B), but if you looked at the graph of B it would have A, B, C and D.
So, if I look at the Clamp example, if I looked at the graph for X then it would look like:

And Tsubasa Chronicles then it would look like:

In this case, each graph is still fairly large, but it is much more readable than before.
There are a few issues that I see with this approach.
1) How are the rules defined? Which relation types do not propagate, ‘other’ and ‘character’ are likely, but what about ‘same setting’? There may even be questions about ‘alternate version’ and ‘alternate setting’.
2) There are probably cases where a ‘character’ or ‘other’ relation should propagate. There are probably cases where ‘other’ was chosen as a link because they didn’t know what to put. A possible example from above would be X2 Double X, It’s graph would look like:

Note that since it only had ‘other’ relations, nothing is propagated; Tokyo Babylon isn’t even listed, even though it is definitely related to X.
3) There are a lot more graphs that need to be created since any anime with ‘other’ or ‘character’ relations needs its own graph generated. [Note this might not be an issue with the new server, and the graphs would be smaller which would help bandwidth.]
After thinking about all of this, I came up with Anime Families, named groups of animes that are related. The idea behind this is when a relation is created between two animes, then the system will ask if the animes are in the same family and if there is not a family name, it will prompt them for the family name. All of the relations for any of the animes in the same family are shown, but relations outside of the family (regardless of the type) do not propagate. In this example I would put, X, X Movie, X2 Double X and Tokyo Babylon in the same family. That would mean that they would share the same graph; it would look X graph above, even if they chose the graph for X2 Double X. Also, the groups could help with the searches as well, for instance if you searched for X, then it could also show Tokyo Babylon because it is in the same family (other examples would be Lost Universe for Slayers or various Pikachu Specials for Pokemon).
There is also the possibility to make subgroups, to group parts of larger groups for organization. For instance this may be applicable for Gundam, but overall it may not be worth the effort for the few families that it would help.
Note the examples I pulled out were just for the sake of explanation and discussion. These relations may not be correct, please do not discuss the validity of these relations here, if they are wrong please discuss it in the DB Change Requests forum.