I know that the documentation states a history_file is available for this
purpose, which I understand, but I'm confused as to what I am supposed to
look for? Is there a certain pattern over a number of iterations that shows
an optimal fit?

Sorry if this is a bit confusing, but I'm very curious with respect to a
kind-of tutorial on how to take the community_structure algorithm, decide
the input values (on the basis of something?), and then determine which
values fit the graph (again, on the basis of something else). My next step
is, of course, to analyse Reichardt and Bornholdt theoretically to try and
make sense of what I need to look for in this algorithm to apply it to
something.

It looks like a very powerful algorithm, but the theoretical basics have me
baffled. Thank you so much for your help!

I know that the documentation states a history_file is available for this
purpose, which I understand, but I'm confused as to what I am supposed to
look for? Is there a certain pattern over a number of iterations that shows
an optimal fit?

The algorithm attempts to minimize the Hamiltonian function defined in
the documentation. Therefore the fit with the lowest value of this
function should be considered the optimal fit.

Sorry if this is a bit confusing, but I'm very curious with respect to a
kind-of tutorial on how to take the community_structure algorithm, decide
the input values (on the basis of something?), and then determine which
values fit the graph (again, on the basis of something else). My next step
is, of course, to analyse Reichardt and Bornholdt theoretically to try and
make sense of what I need to look for in this algorithm to apply it to
something.

It looks like a very powerful algorithm, but the theoretical basics have me
baffled. Thank you so much for your help!

The documentation is no substitute for knowing the
literature... Community detection is a huge field, with new methods and
approaches being developed almost in a weekly basis. I recommend reading
the current review by Santo Fortunato: http://dx.doi.org/10.1016/j.physrep.2009.11.002