Humanity as a Media

If society (mesh) is a collection of communities, and community (polygon) is a collection of relationships, and relationships (edges) are between 2 individuals (vertices), what is a differential, smooth, or continuous community or relationship? "No bumps"? Is there something in differential or continuous game theory which addresses this?  Is there a reason humanity and the math that describes them somehow related? Is learning society through geometry a good idea? Would it be better to learn something more analog alongside our discrete options for human interactions? Let's throw my Facebook community a curve, surface, volume, or hypervolume. I'm starting to see more and more that humanity, is indeed described by shapes. Perhaps humanity is a new form of media, alongside symbol, movie and shape. Hypersocieties? Fractal societies? I guess I should have spent more time in cultural geography.