Great and instructive presentation! Thank you very much for sharing. I assume function IGCommunitiesEdgeBetweenness is defined in your package. But how then it returns this nice object below? Is there a way to create such user-defined object? Any tips on that?

Since version 10 many builtins use such a display. These are called summary boxes. There are internal undocumented functions that make it easy to create a standard looking summary box. But at the time when I implemented this part of the package I wasn't fully comfortable using those, so I made my own imitation. I wanted the implementation to be as future proof as possible.

You can read about how to use either the internal functions or imitate the appearance using only documented functions here:

• http://mathematica.stackexchange.com/q/77658/12

You can also look at the source of IGraph/M:

https://github.com/szhorvat/IGraphM/blob/master/IGraphM/IGraphM.m#L2823

Other than the formatting, IGClusterData objects just wrap an association. Some "properties" then just extract keys from it, others compute something based on what's stored inside.