Stack Exchange recently changed how the Hot Network Questions list works. In a post they mention that each site can limit their exposure to only allow a certain number of questions from a site on the list if the site decides to do that in a meta-question.
Each site can only have a max of five questions on the HNQ list at any given time.
This is a big, much-requested change and we may reduce the number in the future even further. We're starting it higher than some might want (suggestions went as low as one per site) because sites that have had a lot of exposure through the HNQ may see a dramatic drop in visits, so we need to be careful to find the right number here and possibly do some testing at different levels.
This number is also configurable on a per-site basis, so if a site wants to reduce their HNQ footprint, we can lower it even more, even to zero if a site wishes to be excluded entirely. Sites will need to go through a meta discussion before requesting this change and it will be up to the site itself to request a change rather than having the limit imposed upon it (unless we lower the maximum for the entire network). So for example, Stack Overflow can't vote to kick Movies & TV off the list entirely because they don't want to see spoilers for the last season of Game of Thrones, but Movies & TV can ask that fewer of their questions be shown so that they can devote sufficient time to those that are.
Here is the necessary meta question: Do we want to limit the number to something less than five?