Connective eccentricity Cξ(G) = Σ d(v)/ecc(v). Degree over eccentricity: high-degree vertices close to center contribute most. Gupta-Singh-Madan (2000). Opposite of eccentric connectivity (d·ecc). Cξ identifies 'efficient hubs'.
How to Use
Select graph:
- Cξ: Conn. ecc.
- d/ecc: Per vertex
- Hubs: Quality
Cξ vs ECI
ECI = Σ d·ecc (degree × eccentricity). Cξ = Σ d/ecc (degree ÷ eccentricity). ECI rewards peripheral hubs. Cξ rewards central hubs. They give opposing perspectives on vertex importance.
Drug Design
Cξ predicts anti-HIV activity better than many indices. Central, well-connected atoms are drug binding sites. d/ecc captures 'efficiency': high connectivity at short distance from all parts of the molecule.
Step-by-Step Instructions
- 1Select graph.
- 2For each vertex: d(v)/ecc(v).
- 3Sum contributions.
- 4Identify efficient hubs.
- 5Apply to drug design.