Although the circumstances usually involve a reach weapon-wielding rider that's astride a Large mount, fans debate this regularly like in 2011, 2013, 2015, and 2017, yet Paizo has, to my knowledge, never issued any official word.
To sum up, mounted combat does, indeed, say, "For simplicity, assume that you share your mount’s space during combat," but what share means here isn't entirely clear, and no examples are provided. When big and little creatures that are fighting each other share a space, the rules here, for example, cover that eventuality, but the rules don't explain what it means to have the rider share the mount's space.
This fine answer does an excellent job of presenting the traditional conclusion most readers reach. However, this reader would like to offer an alternative approach.
When mounted combat says, "For simplicity, assume that you share your mount’s space during combat," it may mean that a rider shares the entirety of the mount's space, and that would mean all of the squares the mount occupies rather than just its edges. Thus, using this approach, a rider armed with a reach weapon astride a Huge mount threatens using the following diagram:
\begin{array}{c|c}
○ & ○ & ○ & ○ & ○ & ○ & ○ \\ \hline
○ & ○ & ○ & ○ & ○ & ○ & ○ \\ \hline
○ & ○ & • & • & • & ○ & ○ \\ \hline
○ & ○ & • & • & • & ○ & ○ \\ \hline
○ & ○ & • & • & • & ○ & ○ \\ \hline
○ & ○ & ○ & ○ & ○ & ○ & ○ \\ \hline
○ & ○ & ○ & ○ & ○ & ○ & ○ \\
\end{array}
Key: • the Huge mount's space and the squares a rider shares with the Huge mount; ○ the squares that are threatened by a rider that's wielding a reach weapon using this ruling.
This would see the rider threaten 10 ft. from the squares surrounding the mount's central square, and also see the rider threaten the squares 5 ft. around the mount as the rider shares with the mount that dead center square, too.
As previously noted, Pathfinder has been less than forthcoming with clarifications about mounted combat, but this approach does jibe with the ruling put forth by a co-designer of the game on which Pathfinder's is based. Whether or not that ruling's provenance matters—especially as there is no official Pathfinder ruling—is something for an individual group to decide.
Anyway, Pathfinder mounted combat is kind of a mess, and the designers know it: "Mounted combat is underdetailed in Pathfinder," says Pathfinder creative director James Jacobs here. "So, the more you get into it, the more you're going to have to house rule." And, with that in mind, this reader recommends a few mock engagements using both that other answer's approach and this answer's approach, then picking which is preferred. Further, even if the table already agrees that one approach is better, this reader strongly recommends a few mounted combat test runs anyway to get everyone on the same page before trying to incorporate mounted battles into the campaign. The mounted combat rules are vague and complicated, and everyone may have a different opinion on how those rules work.