Augmented eccentric connectivity AECξ(G) = Σ M(v)/ecc(v), where M(v) = Π_{u∈N(v)} d(u). Products of neighbor degrees over eccentricity. Dureja-Madan (2007). Predicts anti-inflammatory activity better than simpler indices.
How to Use
Select graph:
- AECξ: Augmented ECI
- M(v): Neighbor product
- /ecc: Normalize
Computation
For each vertex v: (1) multiply degrees of ALL neighbors → M(v). (2) divide by ecc(v). (3) sum. M(v) is multiplicative: one low-degree neighbor drastically reduces it.
Drug Design
AECξ correlates with anti-inflammatory activity (r²≈0.92 for NSAIDs). Captures both local environment richness (M) and global position (ecc). Dual perspective: local × global.
Step-by-Step Instructions
- 1Select graph.
- 2For each v: M(v) = Πd(neighbors).
- 3Divide by ecc(v).
- 4Sum contributions.
- 5Apply to drug design.