Estrada index EE(G) = Σᵢ e^λᵢ. Weights larger eigenvalues exponentially more. EE = Σₖ (number of closed walks of length k)/k! by Taylor expansion. Captures network structure: branching, folding, centrality. Higher EE = more complex structure.
How to Use
Select graph:
- EE: Estrada index
- e^λ: Per eigenvalue
- Walks: Walk interpretation
Protein Structure
Estrada's original application: protein folding degree. EE measures how 'folded' a molecular graph is. Higher EE = more compact folding. Used to predict protein stability and classify protein families.
Bounds
EE ≥ n (equality iff no edges). EE ≤ n-1+e^(n-1) (K_n achieves maximum). EE(K_n) = n-1+e^(n-1). EE(path) ≈ n·cosh(2/n). Beautiful closed forms for many families.
Step-by-Step Instructions
- 1Select graph.
- 2Find all eigenvalues.
- 3Sum e^λᵢ.
- 4Compare bounds.
- 5Interpret folding.