Editing Bethe lattice (section)

=== Sizes of layers ===
Once a vertex is marked as the root, we can group the other vertices into layers based on their distance from the root. The number of vertices at a distance <math>d>0</math> from the root is <math>z(z-1)^{d-1}</math>, as each vertex other than the root is adjacent to <math>z-1</math> vertices at a distance one greater from the root, and the root is adjacent to <math>z</math> vertices at a distance 1.