  Building on previous work, this paper extends the modeling of political
structures from simplicial complexes to hypergraphs. This allows the analysis
of more complex political dynamics where agents who are willing to form
coalitions contain subsets that would not necessarily form coalitions
themselves. We extend topological constructions such as wedge, cone, and
collapse from simplicial complexes to hypergraphs and use them to study
mergers, mediators, and power delegation in political structures. Concepts such
as agent viability and system stability are generalized to the hypergraph
context, alongside the introduction of the notion of local viability.
Additionally, we use embedded homology of hypergraphs to analyze power
concentration within political systems. Along the way, we introduce some new
notions within the hypergraph framework that are of independent interest.
