Eccentric connectivity index ξᶜ(G) = Σ d(v)·ecc(v). Combines vertex degree (local connectivity) with eccentricity (global position). Sharma-Goswami-Madan (1997). Remarkable predictor of anti-HIV activity, diuretic activity, and anti-inflammatory properties.
How to Use
Select graph:
- ξᶜ: ECI value
- d·ecc: Per vertex
- Drug: Activity
Drug Design
ξᶜ predicts: anti-HIV activity (r²≈0.90), diuretic activity, anti-inflammatory properties, analgesic activity. One of the best single-parameter QSAR predictors for pharmaceutical applications.
Bounds
K_n: ξᶜ = n(n-1) (ecc=1 always). Star: ξᶜ = (n-1)·2 + (n-1)·1 = 3(n-1). Path P_n: ξᶜ computed vertex-by-vertex. Central vertices contribute less.
Step-by-Step Instructions
- 1Select graph.
- 2For each vertex: d(v)·ecc(v).
- 3Sum contributions.
- 4Identify peripheral hubs.
- 5Apply to drug design.