# Exhibit: Barycentric refinement

In the following picture, the Barycentric refinement was done
the classical way, using the coordinate embeddings starting with
a pentagon. The refinement
is abstractly defined for any graph without using any Euclidean
coordinates: take all complete subgraphs as
vertices and connect two such subgraphs, if one is contained in the
other.

See the article,
where we prove a universal spectral behavior of such graphs.