Reciprocal Complementary Wiener Calculator

reciprocal of complementary distance

CalculatorsFreeNo Signup
4.3(556 reviews)
All Tools

Loading tool...

About Reciprocal Complementary Wiener Calculator

A reciprocal complementary Wiener calculator computing RCW(G) = Σ 1/(D+1-d(u,v)) where D = diameter. Ivanciuc (2000). Complementary distances: close pairs (small d) get small weight, far pairs (d≈D) get large weight. Opposite emphasis from Harary. Client-side.

Reciprocal Complementary Wiener Calculator Features

  • RCW(G)
  • 1/(D+1-d)
  • Far-pair
  • Ivanciuc '00
  • Common graphs
Reciprocal complementary Wiener RCW(G) = Σ 1/(D+1-d(u,v)) over all pairs {u,v}. D = diameter. The complement distance D+1-d reverses the scale: close→far, far→close. Then reciprocal emphasizes what was far. Ivanciuc (2000).

How to Use

Select graph:

  • RCW: Recip. comp.
  • D+1-d: Complement
  • vs W: Compare

Complementary Distance

d_c(u,v) = D+1-d(u,v). If d=1 (adjacent): d_c = D. If d=D (diameter pair): d_c = 1. Reversal! Then RCW = Σ1/d_c emphasizes diameter pairs (d_c=1 → contribution=1).

RCW vs Harary

Harary = Σ1/d: emphasizes close pairs. RCW = Σ1/(D+1-d): emphasizes far pairs. Complementary perspectives! Together they give a complete distance picture.

Step-by-Step Instructions

  1. 1Select graph.
  2. 2Compute diameter D.
  3. 3For each pair: D+1-d(u,v).
  4. 4Take reciprocal.
  5. 5Sum all terms.

Reciprocal Complementary Wiener Calculator — Frequently Asked Questions

RCW vs Harary?+

Harary = Σ1/d: close pairs dominate. RCW = Σ1/(D+1-d): far pairs dominate. They are 'complementary' in emphasis. RCW is large when many pairs are at diameter distance.

For K_n (D=1)?+

D+1-d = 1+1-1 = 1 for all pairs. RCW = C(n,2)·1 = n(n-1)/2. Same as Harary for complete graphs! Because complement = identity when D=1.

Chemical use?+

RCW captures far-range molecular interactions. In polymer chains: distant monomer pairs contribute most to overall chain flexibility. Wiener captures near-range, RCW captures far-range.

More Calculators Tools

Explore all 639 other calculators tools available on Generatr

1-Sample Z-Test Calculator2-Sample Z-Test Calculator3D Surface Area CalculatorA/B Testing Significance CalculatorAbsolute Value CalculatorAbundant Number CheckerAccelerated Aging CalculatorAchromatic Number CalculatorAcyclic Chromatic Number CalculatorAdditive Persistence CalculatorAge CalculatorAging Test CalculatorAlbertson Index CalculatorAlgebraic Connectivity CalculatorAliquot Sequence CalculatorAliquot Sum CalculatorAlternating Series Test CalculatorAmicable Number FinderAnnuity CalculatorAPY CalculatorAquarium CO2 Drop CheckerArea CalculatorArea Under Curve CalculatorArithmetic Sequence CalculatorArmstrong Number CalculatorASCVD Risk CalculatorAspect Ratio CalculatorAtom Bond Connectivity CalculatorAugmented Eccentric Connectivity CalculatorAugmented Zagreb Index Calculator
View all 639 calculators tools
Share this tool: