Function Repository Resource:

FactorGraph

Source Notebook

Get a graph representation for the factorization of an integer

Contributed by: Emmanuel Garcés

ResourceFunction["FactorGraph"][n]

gives a graph representing the factorization of the integer n.

ResourceFunction["FactorGraph"][n,pos]

gives the graph for n with the largest factor with position pos.

Details and Options

Let m and n be distinct integers such that m divides n. Then the vertices of a polygon with n vertices can be connected to a polygon with m vertices from m/n equally spaced vertices on the first polygon. This procedure can be applied repeatedly to the prime factors of a number in order to get visualizations of the factorizations of the numbers.

The vertices of a polygon with vertices can be connected to a polygon with vertices from equally spaced vertices on the first polygon. This procedure can be applied repeatedly to the prime factors of a number in order to get visualizations of the factorizations of the numbers.

In ResourceFunction["FactorGraph"][n,pos], pos can be "Inside" or "Outside".

Examples

Basic Examples (5)

Get the rules representing the graph:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

Get the graph:

In[3]:=

Out[3]=

Factor graphs from a list of the first 10 integers:

In[4]:=

$GraphicsGrid[{Table[ GraphPlot[First[ResourceFunction["FactorGraph"][n, "Inside"]], Method -> (n /. {4 -> "RadialDrawing", 6 | 8 | 16 -> "HighDimensionalEmbedding", _ -> "SpringElectricalEmbedding"})], {n, 2, 10}]}, ImageSize -> {800, 100}]$