A more modern take in Political Science is to consider which groups will work with what other groups. Democrats generally don’t work with anarchists, but they will work with democratic socialists (to some extent, anyway), and DemSocs might work with anarchists. Republicans won’t work with democratic socialists, but will work with free market libertarians.

Notably, Horseshoe Theory doesn’t fit into this model. Free market libertarians won’t work with democratic socialists, either. So one way to define the center is to find the centerpoint between all these group connections.

However, another way to look at it is a graph rather than a line. Free market libertarians may not work with Christian nationalists, but both will work with the Republican party (not a perfect example, I admit, but that’s the gist). That graph might not have anything that can be properly called the center.