Theorems · Theorem · combinatorics

Finpartition.coe_energy

∀ {α : Type u_1} [inst : DecidableEq α] {s : Finset α} (P : Finpartition s) (G : SimpleGraph α)
  [inst_1 : DecidableRel G.Adj] {𝕜 : Type u_2} [inst_2 : Field 𝕜] [inst_3 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜],
  ↑(P.energy G) = (∑ uv ∈ P.parts.offDiag, ↑(G.edgeDensity uv.1 uv.2) ^ 2) / ↑P.parts.card ^ 2

Defined in

Mathlib.Combinatorics.SimpleGraph.Regularity.Energy

Cited by

1 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqDecidableRelFieldLinearOrderIsStrictOrderedRing