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Adjacency Matrix Calculator

Work out adjacency matrix instantly with clear inputs, formula shown and shareable results.

About Adjacency Matrix Calculator

An adjacency matrix records a 1 where two vertices are joined. Row sums give the degrees, and raising the matrix to the power k counts walks of length k between every pair of vertices.

Formula

Walk counting

(Aᵏ)ᵢⱼ = number of walks of length k from vertex i to vertex j

Worked example

With the default values below, Adjacency Matrix Calculator returns Number of edges of 5.0. Change any input above and every figure here is recalculated in your browser.

Inputs used

Adjacency matrix rows (row by row)
0,1,1,0 1,0,1,1 1,1,0,1 0,1,1,0
Count walks of this lengthaccepts 1–8
2

Results

Number of edges
5.0
Number of vertices
4
Degree sequence
2, 3, 3, 2
Total walks of the chosen length
26

Step by step

  1. 1Values used
  2. 2Walk counting
  3. 3Number of edges= 5.0
  4. 4Number of vertices= 4
  5. 5Degree sequence= 2, 3, 3, 2
  6. 6Total walks of the chosen length= 26

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 1 decimal place, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For the sample 4×4 matrix?

Degrees are 2, 3, 3, 2 summing to 10, so there are 5 edges, and A² totals 26 walks of length two.

How do I spot a directed graph?

Its matrix is not symmetric, so an entry can be 1 in one direction and 0 in the other.

Related Calculators

Adjacency Matrix Calculator – Calculate Number of edges