Szeged Index Calculator

distance-partitioning index

CalculatorsFreeNo Signup
4.8(757 reviews)
All Tools

Loading tool...

About Szeged Index Calculator

A Szeged index calculator computing Sz(G) = Σ_{e=(i,j)} n_i(e)·n_j(e) where n_i(e) = vertices closer to i than j. Gutman (1994). Generalization of Wiener index for non-trees. Sz ≥ W always. Sz = W iff bipartite. Client-side.

Szeged Index Calculator Features

  • Sz(G)
  • nᵢ·nⱼ
  • ≥ Wiener
  • Bipartite
  • Common graphs
Szeged index Sz(G) = Σ nᵢ(e)·nⱼ(e). For each edge e=(i,j): count vertices closer to i vs closer to j. Multiply counts. Sum over all edges. Gutman (1994). Sz ≥ W (Wiener) always. Sz = W iff G is bipartite (no odd cycles)!

How to Use

Select graph:

  • Sz: Szeged index
  • nᵢ·nⱼ: Per edge
  • Sz vs W: Compare

Sz vs Wiener

For trees: Sz = W (bipartite, no equidistant vertices). For non-bipartite: Sz > W. The gap Sz-W measures 'non-bipartiteness'. The revised Szeged index also counts equidistant vertices.

Applications

QSAR: Sz correlates with molecular properties. Network analysis: edge-centric distance measure. Captures how each edge 'divides' the graph into two sides. Graph partitioning quality metric.

Step-by-Step Instructions

  1. 1Select graph.
  2. 2For each edge: count nᵢ, nⱼ.
  3. 3Multiply nᵢ·nⱼ.
  4. 4Sum over edges.
  5. 5Compare with W.

Szeged Index Calculator — Frequently Asked Questions

Why is Sz ≥ W always?+

For trees, every vertex is strictly closer to one endpoint (bipartite). For non-trees, some vertices are equidistant — they don't count in nᵢ or nⱼ. This 'missing' contribution makes W use smaller factors.

What does nᵢ(e) mean?+

For edge e=(u,v): nᵤ(e) = number of vertices w with d(w,u) < d(w,v). These vertices are 'on u's side' of the edge. The edge divides the graph into two influence zones.

What is the revised Szeged index?+

Revised Sz: vertices equidistant to both endpoints are split equally between nᵢ and nⱼ. Fixes the 'missing vertex' problem. For bipartite: unchanged. For non-bipartite: Sz_rev < Sz.

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: