  In the companion paper~\cite{paper1}, we use classical measures based on
force probability density functions (PDFs), as well as Betti numbers
(quantifying the number of components, related to force chains, and loops), to
describe the force networks in tapped systems of disks and pentagons. In the
present work, we focus on the use of persistence analysis, that allows to
describe these networks in much more detail. This approach allows not only to
describe, but also to quantify the differences between the force networks in
different realizations of a system, in different parts of the considered
domain, or in different systems. We show that persistence analysis clearly
distinguishes the systems that are very difficult or impossible to
differentiate using other means. One important finding is that the differences
in force networks between disks and pentagons are most apparent when loops are
considered: the quantities describing properties of the loops may differ
significantly even if other measures (properties of components, Betti numbers,
or force PDFs) do not distinguish clearly the investigated systems.
