Neighborhood Randic Calculator

second-order Randić index

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About Neighborhood Randic Calculator

A neighborhood Randić index calculator computing NR(G) = Σ_{(u,v)∈E} 1/√(S(u)·S(v)) where S(v) = Σ d(neighbors). Mondal-De-Pal (2019). Second-order Randić: replaces degree product with S-product. More discriminating than classical R. Client-side.

Neighborhood Randic Calculator Features

  • NR(G)
  • 1/√(S·S)
  • 2nd-order
  • Mondal '19
  • Common graphs
Neighborhood Randić NR(G) = Σ 1/√(S(u)·S(v)) over edges. Second-order Randić: uses neighborhood degree sums instead of degrees. Mondal-De-Pal (2019). NR is smaller than R (since S≥d) but much more discriminating.

How to Use

Select graph:

  • NR: Neighbor Randić
  • 1/√(SS): Per edge
  • vs R: Compare

NR vs R

R = Σ1/√(dd): first-order. NR = Σ1/√(SS): second-order. Since S≥d, we have SS≥dd, so 1/√(SS) ≤ 1/√(dd). Thus NR ≤ R always.

Discrimination

Classical R is determined by degree sequence. NR goes beyond: uses neighborhood structure. Two degree-regular graphs can have different NR if their neighborhoods differ. Breaks degree-sequence equivalence.

Step-by-Step Instructions

  1. 1Select graph.
  2. 2Compute S(v) for each vertex.
  3. 3For each edge: 1/√(S(u)·S(v)).
  4. 4Sum all terms.
  5. 5Compare with R.

Neighborhood Randic Calculator — Frequently Asked Questions

NR always ≤ R?+

Yes! S(v) ≥ d(v) for all v (S sums neighbor degrees, which are each ≥1, and there are d(v) of them, but S also includes their actual degrees). So S-products ≥ d-products, and reciprocal roots reverse the inequality.

When NR helps over R?+

When degree sequence alone doesn't distinguish graphs. Regular graphs: R = m/d (same for all d-regular). NR varies based on neighborhood structure. NR breaks the 'regular graph blind spot' of R.

Computational cost?+

O(m + Σd(v)) = O(m + n): compute S(v) in one pass over edges, then NR in one pass over edges. Same complexity as R, just a preprocessing step for S values.

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