What exactly is "chromosome topology"?
I think that there are a few things going on in this question, I'm going to try to answer the ones that I think are most pertinent:

We should not expect &quot;topology&quot; as used in the Hi-C field to have a rigorous mathematical interpretation. Most of the people thinking about it are ultimately biologists who are interested in biological problems. As suggested in the comments, they are basically interested in the shape of DNA in the cell; e.g. which pieces of DNA are close together and which are far away. You can use this information for a lot of different purposes of course, but most people using the technique are satisfied with viewing topology as &quot;the set of pairwise distances between all DNA chunks&quot; (and whatever things you can infer from that set).

Your sense (from the comment) that the linear chromosome ordering is the main interesting feature of topology is (IMO) absolutely correct. However, it is not a given that every chromosome is put together the same way. This is related to the most useful application of Hi-C data that I know of, which is to either (A) scaffold genomes (put discontinuous sequences into the right order) or (B) deconvolute mixed populations of genomes into groups of sequences that belong to the same cell. The linear order of DNA is by at least an order of magnitude the dominant signal in the data, and is therefore the most trustworthy thing in there.

Network topology is sometimes implicit but generally central as a feature of algorithms using Hi-C data. I don't know that we can say that all workers in the field are thinking of this when they talk about topology, but I certainly am. Some random papers that make it fairly obvious: here, here, here.


(Full disclosure: I work for a company that sells Hi-C kits and services.)