Mathematics · Discrete Mathematics
Graph Community Modularity Excess null-model expected fraction Solver
Rearrange the graph community modularity excess relationship and solve for null-model expected fraction.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use b=a−c with modularity contribution=0.15000000000000002 and observed within-community edge fraction=0.46.
- null-model expected fraction=0.31.
- Substitution into c=a−b reconstructs 0.15000000000000002.
Understand Graph Community Modularity Excess: solve null-model expected fraction
One idea, three depths
Choose how deeply to explain Graph Community Modularity Excess: solve null-model expected fraction
Graph Community Modularity Excess: solve null-model expected fraction: Rearrange the graph community modularity excess relationship and solve for null-model expected fraction.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Graph Community Modularity Excess: solve null-model expected fraction to answer this question: rearrange the graph community modularity excess relationship and solve for null-model expected fraction? Enter modularity contribution and observed within-community edge fraction; the calculator shows null-model expected fraction. For example: observed within-community edge fraction=0.46 and null-model expected fraction=0.31 produce modularity contribution=0.15000000000000002. The answer tells you null-model expected fraction.
Age 15Explain it to a 15-year-oldConnect it to the formula
A modularity contribution is observed within-community edge fraction minus its null-model expectation. This page isolates null-model expected fraction and verifies it in the original relationship. The rule is b=a−c. Its input values are modularity contribution, observed within-community edge fraction, and the main result is null-model expected fraction. For example: observed within-community edge fraction=0.46 and null-model expected fraction=0.31 produce modularity contribution=0.15000000000000002.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated graph community modularity excess: solve null-model expected fraction relation over the valid real-number domain stated below. The implemented relation is b=a−c, evaluated from modularity contribution, observed within-community edge fraction to produce null-model expected fraction. A modularity contribution is observed within-community edge fraction minus its null-model expectation. This page isolates null-model expected fraction and verifies it in the original relationship. The null model and normalization must match those used for the observed fraction.
Inputs and valid domain
- modularity contribution must be a finite real number.
- observed within-community edge fraction must be a finite real number.
Important boundary: The null model and normalization must match those used for the observed fraction.
The formula
b=a−c
How the calculator works through it
It substitutes modularity contribution, observed within-community edge fraction into the formula and exposes every numerical step above. The main output is null-model expected fraction, accompanied by Reconstructed modularity contribution.
Read the result correctly
The null-model expected fraction is the direct answer to “rearrange the graph community modularity excess relationship and solve for null-model expected fraction.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
observed within-community edge fraction=0.46 and null-model expected fraction=0.31 produce modularity contribution=0.15000000000000002.
Where this model stops being reliable
The null model and normalization must match those used for the observed fraction.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Graph Community Modularity Excess: solve null-model expected fraction works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Graph Community Modularity Excess: solve null-model expected fraction uses b=a−c. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Sets, membership and finite collections
Sets provide the objects and membership rules that give Graph Community Modularity Excess: solve null-model expected fraction its discrete meaning.
Review this foundation about 6 min
Optional enrichment
- Ordered arrangements
Permutations connect Graph Community Modularity Excess: solve null-model expected fraction to systematic counting and arrangement problems.
Review this foundation about 5 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read modularity contribution, observed within-community edge fraction.
- Evaluate the principal relationship: b=a−c.
- Return null-model expected fraction and check the domain conditions described above.
Python
from math import *
def graph_modularity_excess_solve_b(c, a) -> float:
return (a - c)
assert abs(graph_modularity_excess_solve_b(0.15000000000000002, 0.46) - 0.31) < 1e-6 * max(1.0, abs(0.31))
C
#include <assert.h>
#include <math.h>
double graph_modularity_excess_solve_b(double c, double a) {
return (a - c);
}
int main(void) {
const double expected = 0.31;
const double actual = graph_modularity_excess_solve_b(0.15000000000000002, 0.46);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double graph_modularity_excess_solve_b(double c, double a) {
return (a - c);
}
int main() {
constexpr double expected = 0.31;
const double actual = graph_modularity_excess_solve_b(0.15000000000000002, 0.46);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double graph_modularity_excess_solve_b(double c, double a)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global graph_modularity_excess_solve_b
section .text
graph_modularity_excess_solve_b:
push rbp
mov rbp, rsp
sub rsp, 32
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-16]
subsd xmm0, [rbp-8]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = graph_modularity_excess_solve_b(c, a)
result = (a - c);
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[c_, a_] := (a - c);
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Graph Community Modularity Excess null-model expected fraction Solver. MW SysArc Tools. https://math.mwsysarc.com/discrete-mathematics/graph-modularity-excess-null-model-expected-fraction-solver
MLA 9
MW SysArc. “Graph Community Modularity Excess null-model expected fraction Solver.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/discrete-mathematics/graph-modularity-excess-null-model-expected-fraction-solver. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Graph Community Modularity Excess null-model expected fraction Solver.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/discrete-mathematics/graph-modularity-excess-null-model-expected-fraction-solver.
Harvard
MW SysArc (2026) ‘Graph Community Modularity Excess null-model expected fraction Solver’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/discrete-mathematics/graph-modularity-excess-null-model-expected-fraction-solver (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_graph_modularity_excess_solve_b_2026,
author = {{MW SysArc}},
title = {Graph Community Modularity Excess null-model expected fraction Solver},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/discrete-mathematics/graph-modularity-excess-null-model-expected-fraction-solver},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Graph Community Modularity Excess null-model expected fraction Solver
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/discrete-mathematics/graph-modularity-excess-null-model-expected-fraction-solver
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Graph Community Modularity Excess: solve null-model expected fraction do?
Rearrange the graph community modularity excess relationship and solve for null-model expected fraction.
How does the Graph Community Modularity Excess: solve null-model expected fraction work?
The calculator applies b=a−c. A modularity contribution is observed within-community edge fraction minus its null-model expectation. This page isolates null-model expected fraction and verifies it in the original relationship.
What can I learn from the Graph Community Modularity Excess: solve null-model expected fraction?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .