Characterize when clique and Dowker constructions diverge

Characterize which properties of co-occurrence data—specifically density, group-size distribution, and closure—make the clique and Dowker constructions diverge, and determine the magnitude of that divergence.

Background

The paper proves that, for observed-group data, the clique complex can erase first-homology classes that remain in the Dowker complex, but the empirical size of this loss varies across data sets.

An unresolved question is which structural properties of the data predict substantial disagreement between the two constructions and how much the choice of construction will affect the resulting topology. The authors state that answering this question would allow analysts to estimate the importance of the construction choice in advance.