2025/09/04 by Jojić, Duško, Šarčević, Franjo
#05A99 #91C99 #91F10 #FOS: Physical sciences #Physics and Society (physics.soc-ph)
paper · doi:10.48550/arxiv.2509.04249
Modeling political structures by simplicial complexes, we investigate whether introducing a mediator into a substructure increases or decreases the stability of the overall structure. We prove theorems that quantify the stability of a political structure when n mediators are introduced, either one by one or simultaneously. We also examine how the stability is affected when a single agent is split into two. In addition, stability is expressed in terms of the h-vector, and special attention is given to a class of political structures modeled by shellable simplicial complexes. In the latter context, we analyze weighted political structures and examples of political structures modeled by independence complexes of graphs.