Degree Deviation Calculator

total degree deviation from mean

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About Degree Deviation Calculator

A degree deviation calculator computing S(G) = Σ |d(v) - d̄| where d̄ = 2m/n. Total absolute deviation of degrees from the mean. S = 0 iff regular. Related to Bell B (variance) via S² ≤ n·B (Cauchy-Schwarz). Client-side.

Degree Deviation Calculator Features

  • S(G)
  • Σ|d-d̄|
  • S=0↔reg.
  • MAD
  • Common graphs
Degree deviation S(G) = Σ |d(v)-d̄|. The MAD (mean absolute deviation) of the degree sequence, scaled by n. S = 0 ⟺ regular. Simpler than variance B but less sensitive. Related: S² ≤ n·n·B (by Cauchy-Schwarz on |d-d̄|).

How to Use

Select graph:

  • S: Total deviation
  • d̄: Mean degree
  • vs B: Compare

Statistical View

S/n = MAD (mean absolute deviation). √B = standard deviation σ. MAD ≤ σ always. S captures the 'typical' deviation. B captures the 'squared' deviation. Different robustness properties.

Bounds

0 ≤ S ≤ 2m(n-2)/n. Star maximizes S among trees. S/n is the average deviation per vertex.

Step-by-Step Instructions

  1. 1Select graph.
  2. 2Compute d̄ = 2m/n.
  3. 3For each v: |d(v)-d̄|.
  4. 4Sum all terms.
  5. 5Compare S/n with √B.

Degree Deviation Calculator — Frequently Asked Questions

S vs Bell B?+

B = (1/n)Σ(d-d̄)². S = Σ|d-d̄|. B uses squared deviations (more sensitive to outliers). S uses absolute deviations (more robust). Statisticians debate which is better!

S for star?+

Hub: |n-1 - (2(n-1)/n)| = |(n-1)(n-2)/n|. Leaves: |1 - 2(n-1)/n| = |(n-2)/n|. S = (n-1)(n-2)/n + (n-1)(n-2)/n = 2(n-1)(n-2)/n.

MAD vs σ?+

MAD = S/n (mean abs deviation). σ = √B (standard deviation). Always MAD ≤ σ. Equality iff all |d-d̄| are equal, which for degrees means binary (two distinct values).

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