Peripheral Wiener Index Calculator

boundary vertex distance sum

CalculatorsFreeNo Signup
4.9(686 reviews)
All Tools

Loading tool...

About Peripheral Wiener Index Calculator

A peripheral Wiener index calculator computing PW(G) = Σ d(pᵢ,pⱼ) over all peripheral vertex pairs (vertices with ecc = diam). Complements terminal Wiener (leaves). PW focuses on the 'boundary' of the graph. Client-side.

Peripheral Wiener Index Calculator Features

  • PW(G)
  • Peripheral
  • ecc=diam
  • Boundary
  • Common graphs
Peripheral Wiener PW(G) = Σ d(pᵢ,pⱼ) for peripheral vertex pairs (ecc = diam). Only measures distances between the 'boundary' vertices — those at maximum eccentricity. PW captures how spread out the graph's periphery is.

How to Use

Select graph:

  • PW: Peripheral W.
  • ecc=diam: Boundary
  • vs TW: Compare

PW vs TW

Terminal Wiener: distances between leaves (degree-1). Peripheral Wiener: distances between peripheral vertices (max eccentricity). Different concepts! A leaf may not be peripheral. A peripheral vertex may not be a leaf.

Self-Centered Graphs

Self-centered: ALL vertices are peripheral (ecc = diam everywhere). Then PW = W! Examples: K_n, C_n. PW provides maximum information for non-self-centered graphs.

Step-by-Step Instructions

  1. 1Select graph.
  2. 2Find peripheral vertices.
  3. 3Compute pairwise distances.
  4. 4Sum boundary distances.
  5. 5Compare with W.

Peripheral Wiener Index Calculator — Frequently Asked Questions

What are peripheral vertices?+

Vertices with eccentricity = diameter. They're 'as far as possible' from some other vertex. The graph's boundary. In trees: always the leaves of the longest path.

PW vs W?+

W: all pairs. PW: only peripheral-peripheral pairs. PW/W measures 'boundary contribution'. For self-centered graphs: PW = W. For trees: PW often much smaller than W.

When is PW most useful?+

PW characterizes the 'shape of the boundary'. Round molecules: PW small (peripheral atoms close). Linear: PW large (peripheral atoms far). Useful for molecular shape classification.

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: