Is there connection betwwen simplex and complete/almost complete/dense graphs? Can any complete or dense graph be expressed as special case of some simplex or complex?
I am actively searching methods how to enumerated/represent nodes of dense or complete graphs with order to model dynamics on such graphs. Maybe every duch graph can be expressed as simplex and maybe simplices have such effective methodes for enumeration of nodes? Maybe there is even some research about (Hamiltonian) dynamics on simplices?
Technically any graph can be represented as a simplicial complex - whether it is beneficial to represent the cliques in dense graphs as simplices is entirely dependent on your use case.