Rank of Incidence Matrix Calculator

✖Nodes is defined as the junctions where two or more elements are connected.ⓘ Nodes [N]

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✖The Matrix Rank refers to the number of linearly independent rows or columns in the matrix.ⓘ Rank of Incidence Matrix [ρ]

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Formula

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Rank of Incidence Matrix

Formula

`"ρ" = "N"-1`

Example

`"5"="6"-1`

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Rank of Incidence Matrix Solution

STEP 0: Pre-Calculation Summary

Formula Used

Matrix Rank = Nodes-1
ρ = N-1
This formula uses 2 Variables

Variables Used

Matrix Rank - The Matrix Rank refers to the number of linearly independent rows or columns in the matrix.
Nodes - Nodes is defined as the junctions where two or more elements are connected.

STEP 1: Convert Input(s) to Base Unit

Nodes: 6 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ρ = N-1 --> 6-1

Evaluating ... ...

ρ = 5

STEP 3: Convert Result to Output's Unit

5 --> No Conversion Required

FINAL ANSWER

5 <-- Matrix Rank

(Calculation completed in 00.020 seconds)

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Credits

Created by swetha samavedam

Delhi Technological University (DTU), delhi

swetha samavedam has created this Calculator and 10+ more calculators!

Verified by Pinna Murali Krishna

Lovely professional university (LPU), Phagwara,Punjab

Pinna Murali Krishna has verified this Calculator and 7 more calculators!

< 15 Circuit Graph Theory Calculators

Average Path Length between Connected Nodes

Go Average Path Length = ln(Nodes)/ln(Average Degree)

Number of Branches in Forest Graph

Go Forest Graph Branches = Nodes-Forest Graph Components

Number of Branches in any Graph

Go Simple Graph Branches = Simple Graph Links+Nodes-1

Number of Links in any Graph

Go Simple Graph Links = Simple Graph Branches-Nodes+1

Number of Nodes in any Graph

Go Nodes = Simple Graph Branches-Simple Graph Links+1

Average Degree

Go Average Degree = Node Connection Probability*Nodes

Rank for Incidence Matrix using Probability

Go Matrix Rank = Nodes-Node Connection Probability

Number of Branches in Complete Graph

Go Complete Graph Branches = (Nodes*(Nodes-1))/2

Number of Graphs given Nodes

Go Number of Graph = 2^(Nodes*(Nodes-1)/2)

Spanning Tress in Complete Graph

Go Spanning Trees = Nodes^(Nodes-2)

Number of Maxterms and Minterms

Go Total Minterms/ Maxterms = 2^Number of Input Variables

Maximum Number of Edges in Bipartite Graph

Go Bipartite Graph Branches = (Nodes^2)/4

Number of Branches in Wheel Graph

Go Wheel Graph Branches = 2*(Nodes-1)

Rank of Incidence Matrix

Go Matrix Rank = Nodes-1

Rank of Cutset Matrix

Go Matrix Rank = Nodes-1

Rank of Incidence Matrix Formula

Matrix Rank = Nodes-1
ρ = N-1

What is an Incidence matrix?

Incidence matrix is that matrix which represents the graph such that with the help of that matrix we can draw a graph. If from a given incidence matrix, any arbitrary row is deleted, then the new matrix formed will be reduced incidence matrix.

How to Calculate Rank of Incidence Matrix?

Rank of Incidence Matrix calculator uses Matrix Rank = Nodes-1 to calculate the Matrix Rank, The rank of incidence matrix is (n-1), where n is the number of nodes of the graph. The order of incidence matrix is (n × b), where b is the number of branches of graph. Matrix Rank is denoted by ρ symbol.

How to calculate Rank of Incidence Matrix using this online calculator? To use this online calculator for Rank of Incidence Matrix, enter Nodes (N) and hit the calculate button. Here is how the Rank of Incidence Matrix calculation can be explained with given input values -> 5 = 6-1.

FAQ

What is Rank of Incidence Matrix?

The rank of incidence matrix is (n-1), where n is the number of nodes of the graph. The order of incidence matrix is (n × b), where b is the number of branches of graph and is represented as ρ = N-1 or Matrix Rank = Nodes-1. Nodes is defined as the junctions where two or more elements are connected.

How to calculate Rank of Incidence Matrix?

The rank of incidence matrix is (n-1), where n is the number of nodes of the graph. The order of incidence matrix is (n × b), where b is the number of branches of graph is calculated using Matrix Rank = Nodes-1. To calculate Rank of Incidence Matrix, you need Nodes (N). With our tool, you need to enter the respective value for Nodes and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Matrix Rank?

In this formula, Matrix Rank uses Nodes. We can use 2 other way(s) to calculate the same, which is/are as follows -

Matrix Rank = Nodes-1
Matrix Rank = Nodes-Node Connection Probability

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