In some of the literature relating to hypergraph applications, there is an argument about information loss when representing data as a graph compared to a hypergraph.
For example, the well known paper by Zhou et al (2006) show a toy example of a graph and a hypergraph constructed from the same adjacency matrix. I have reproduced Figure 1 from this paper below:
The authors argue that with the graph representation 'we obviously miss the information on whether the same person joined writing three or more articles or not. Such information loss is unexpected...'.
This idea of information loss is interesting to me and I set out to try and quantify precisely how one could measure such information loss between a graph and a hypergraph (in this particular case an undirected, binary graph versus an undirected hypergraph).
However, I can find no literature addressing this problem.
Can anyone advise where one might look for solutions?