Wolfram Language Paclet Repository

Community-contributed installable additions to the Wolfram Language

Primary Navigation

    • Cloud & Deployment
    • Core Language & Structure
    • Data Manipulation & Analysis
    • Engineering Data & Computation
    • External Interfaces & Connections
    • Financial Data & Computation
    • Geographic Data & Computation
    • Geometry
    • Graphs & Networks
    • Higher Mathematical Computation
    • Images
    • Knowledge Representation & Natural Language
    • Machine Learning
    • Notebook Documents & Presentation
    • Scientific and Medical Data & Computation
    • Social, Cultural & Linguistic Data
    • Strings & Text
    • Symbolic & Numeric Computation
    • System Operation & Setup
    • Time-Related Computation
    • User Interface Construction
    • Visualization & Graphics
    • Random Paclet
    • Alphabetical List
  • Using Paclets
    • Get Started
    • Download Definition Notebook
  • Learn More about Wolfram Language

UndirectedGraphs

Guides

  • GraphConstructionandRepresentation
  • Graph Functions
  • GraphOperationsandModifications
  • GraphPropertiesAndMeasurements
  • GraphVisualization
  • Paths, Cycles, and Flows
  • Computation on Graphs

Symbols

  • AlternatingTreeGraph
  • BananaTreeGraph
  • BookGraph
  • CoboundaryPolynomial
  • CombGraph
  • FirecrackerGraph
  • GearGraph
  • GeneralizedTriangularGridGraph
  • Girth
  • GraphicalDegreeSequenceQ
  • HelmGraph
  • IndependencePolynomial
  • KayakPaddleGraph
  • LadderRungGraph
  • PanGraph
  • PositiveIntegerQ
  • RankPolynomial
  • ReliabilityPolynomial
  • ResistanceMatrix
  • SunletGraph
  • TadpoleGraph
  • VertexCoordinateList
  • VertexInsert
PeterBurbery`UndirectedGraphs`
RankPolynomial
​
RankPolynomial
[graph]
computes the rank polynomial of
graph
.
​
​
RankPolynomial
[graph,{
indeterminate
1
,
indeterminate
2
}]
computes the rank polynomial of
graph
with the indeterminates
indeterminate
i
.
​
Details and Options

Examples  
(1)
Basic Examples  
(1)
Two rank polynomials:
In[1]:=
RankPolynomial

BananaTreeGraph
[{7,21}]
Out[1]=
147
(1+x.)
In[2]:=
RankPolynomial

BookGraph
[7]
Out[2]=
1+22x.+231
2
x.
+126
4
x.
(58+y.)+7
3
x.
(220+y.)+21
5
x.
1248+52y.+
2
y.
+63
6
x.
1167+95y.+5
2
y.
+
7
x.
164538+22995y.+2240
2
y.
+35
3
y.
+6
8
x.
49410+10836y.+1645
2
y.
+70
3
y.
+63
10
x.
7911+3537y.+1011
2
y.
+125
3
y.
+5
4
y.
+7
9
x.
61452+19764y.+4245
2
y.
+335
3
y.
+5
4
y.
+21
11
x.
21546+12825y.+4680
2
y.
+825
3
y.
+61
4
y.
+
5
y.
+63
12
x.
4941+3780y.+1710
2
y.
+405
3
y.
+47
4
y.
+2
5
y.
+7
13
x.
21870+20898y.+11475
2
y.
+3510
3
y.
+585
4
y.
+46
5
y.
+
6
y.
+3
14
x.
16038+18711y.+12285
2
y.
+4725
3
y.
+1071
4
y.
+133
5
y.
+7
6
y.
+
15
x.
7290+10206y.+7938
2
y.
+3780
3
y.
+1134
4
y.
+210
5
y.
+22
6
y.
+
7
y.

Change the indeterminate:
In[3]:=
RankPolynomial

BookGraph
[7],{p.,q.}
Out[3]=
1+22p.+231
2
p.
+126
4
p.
(58+q.)+7
3
p.
(220+q.)+21
5
p.
1248+52q.+
2
q.
+63
6
p.
1167+95q.+5
2
q.
+
7
p.
164538+22995q.+2240
2
q.
+35
3
q.
+6
8
p.
49410+10836q.+1645
2
q.
+70
3
q.
+63
10
p.
7911+3537q.+1011
2
q.
+125
3
q.
+5
4
q.
+7
9
p.
61452+19764q.+4245
2
q.
+335
3
q.
+5
4
q.
+21
11
p.
21546+12825q.+4680
2
q.
+825
3
q.
+61
4
q.
+
5
q.
+63
12
p.
4941+3780q.+1710
2
q.
+405
3
q.
+47
4
q.
+2
5
q.
+7
13
p.
21870+20898q.+11475
2
q.
+3510
3
q.
+585
4
q.
+46
5
q.
+
6
q.
+3
14
p.
16038+18711q.+12285
2
q.
+4725
3
q.
+1071
4
q.
+133
5
q.
+7
6
q.
+
15
p.
7290+10206q.+7938
2
q.
+3780
3
q.
+1134
4
q.
+210
5
q.
+22
6
q.
+
7
q.

SeeAlso
TuttePolynomial
RelatedGuides
▪
Computation on Graphs
""

© 2025 Wolfram. All rights reserved.

  • Legal & Privacy Policy
  • Contact Us
  • WolframAlpha.com
  • WolframCloud.com