Please please please do not rely on these online back link sites! They are God awful!! If you really need to know what is going on, you will have to do it yourself.
I suggest that people keep http://www.screamingfrog.co.uk/seo-spider/ in their arsenal/tool box. It comes in handy. I do not recommend too many tools, in fact, I tend to avoid it, but this is one that everyone should not only be aware of, but at least keep a current download of on their hard-drive if it is not installed.
You may have to pay for a license for a site your size, but you can at least try it before you buy and the prices is not huge.
Screaming Frog is a spider that does direct highly detailed analysis against a website for the price of some entries in your log file. It sounds like a necessary tool in your case. Having 50,000 links between sites especially to one page/resource will catch up to you and cause you heart-burn and regret. It can cost you your rankings in the SERPs potentially so this is a very important problem to solve as quickly as you can. This tool should find the problem for you and perhaps others you are unaware of very very quickly.
It occurred to me that a little explanation is in order. It has been a decade or more since I have had to explain this part of search, but this seemed like a good time to do so. So if I do not do as stellar a job as you and I like, please forgive an old man who has not had to think about this topic for a very very long time.
In search, there is the term realm. A realm is a simple concept to understand.
subc.a.example are all one realm. Simple huh? It is essentially all sites that belong to a single parent domain. In the case of a realm, you have one set of contacts within whois and one owner of the site. You can draw a cloud around this. Links within a single realm follow patterns. It would not necessarily be a bad thing if there are numerous links from
products.a.example. But consider this, links would again follow certain traditional patterns. 20,000 links from
products.a.example could fit this pattern if it is a site-wide templated link in the navigation, header, or footer. This would make sense. There is a reason why I mention this.
b.example are two separate realms even though they share the same contacts and owner. This would be two clouds, however, since the whois data is relatively if not exactly the same, the search engine can draw a strong link between the two realms as being related.
Keep in mind that link patterns are machine learned. Any machine learning must be seeded, ie. taught (AI artificial intelligence). This is done with human intervention and the seed data can be removed at any point once the machine learning has begun. So for link patterns, a great number of sites and realms have been evaluated and some human intervention (teaching) is given to mark some of these patterns as being indicative of something.
b.example has 20,000 links to
a.example then a red flag is raised. However, since there is a linkage in contacts and ownership, a different set of patterns is used to evaluate the links than sites within the same realm. In this case,
b.example is branded similarly as
a.example and the links are in the navigation. Okay. This fits a traditional but slightly unusual pattern. It makes sense, however, the phenomenon is noted.
But lets say that
panther.a.example also has 20,000 links to
a.example. These links are evaluated. They are all to the same resource and are not linked in areas/ways where machine learning has noted as traditional. A red flag is raised. Since this is an unusual pattern, the two realms are further evaluated for link patterns.
Let's say that this is all that is found and no linking scheme is determined. Okay then. The two realms remain within the system to be further evaluated for a linking scheme until the trigger is removed that raised the red flag.
In the case of
xxxlinks.example these are two realms with no relationship. Why did I bring this up? Simple.
xxxlinks.example as made 20,000 links to
a.example. This is a problem. However, search engines have in the past years noted who does this form and other forms of linking and has put them into a category of a sites to be understood as something. Search engines do make some distinctions. An outbound linking pattern is developed for
xxxlinks.example and it belongs to a group of sites that creates outbound links unrelated to the sites that it links to. Okay. Understood. It is not the fault of
xxxlinks.example has created so many links. Forgiven at least within a limit. Simple enough. The search engine will keep both realms within it's system to be evaluated.
But now we look at
g.example. These realms have different whois data, but past registration information does link them by one contact e-mail address. Huh. Interesting. Now they all have private registrations from a company known for not vetting the whois/customer data for validity. Because of the one e-mail address, a link is made between these realms. Because of the nature of the link, the link is marked as suspect. There are 20,000 links between these sites. A red flag is raised. It is determined that these links follow a pattern that indicates a rank manipulation scheme. Problem.
But what has this last example have to do with our earlier example? Simple. Both are in the system and constantly being evaluated. We do not know what triggers there are and when a pattern is considered enough to mark a realm as being manipulative. If a realm is determined to be suspect, then the realms will see their links lower in the SERPs. However, if the realm is determined to be more than suspect, then the realms may not see SERP links at all.
And this is why the 50,000 links must be understood, evaluated, and potentially removed if they do not make sense.