Represent a correlation matrix via a graph

Questions
1

I have a simple (maybe mistake!) question. Is it possible to present a correlation matrix via a graph?
For example:

data1 = {11.22, 12.29, 12.97, 14.15, 17.33, 17.60, 16.62, 14.43, 
   13.62, 11.01};
data2 = {12.29, 12.97, 14.15, 17.33, 17.60, 16.625`, 14.43, 13.62, 
   11.01, 9.25};
data3 = {12.97, 14.15, 17.33, 17.60, 16.625`, 14.43, 13.62, 11.016, 
   9.25, 9.48};

Apply[Correlation, 
  Tuples[{data1, data2, data3}, 2] // Partition[#, 3, 3] &, {2}] // 
 MatrixPlot[#, ColorFunction -> "DeepSeaColors", 
   PlotLegends -> Automatic] &

8969Untitled.png
8969Untitled.png701Ă—578 5.45 KB

Thank you for your help.

2

If you allow for edges to have custom weights, then I’m pretty sure that yes you can represent a correlation matrix with a directed graph. However, if you just label the edges with their weights, it may be challenging to visualize. It would be easy to include/omit edges if the correlation matrix was binary. Changing the thickness or opacity of the edges with their weights would be the best way to visualize a correlation matrix as a graph in my opinion.

3

Along the lines that Joseph suggested

corr = Apply[Correlation, Tuples[{data1, data2, data3}, 2] // Partition[#, 3, 3] &, {2}]

WeightedAdjacencyGraph[corr,
 DirectedEdges -> True,
 EdgeStyle -> {DirectedEdge[i_, j_] :> AbsoluteThickness[corr[[i, j]]]},
 PlotTheme -> "Scientific"]

9870plot.png
9870plot.png450Ă—392 15.6 KB

4

Thank you, Joseph.

May I ask you to do for the example data? Is the result understandable?

5

Wow!

Thank you so much, man.

For more understanding, is it possible to show correlation values on the figure?

6

Please read the rules: http://wolfr.am/READ-1ST
New questions require new discussions posted separately and not digressing topics of other discussions. This question was moved to its own new discussion.

7

@Alex Teymouri the questions you are asking are easily found in documentation. As you can read in the forum rules you should show your own effort first and explain what does and what does not work in your own code. Good places to start:

8

As Sam said, this can be easily found in the documentation.

rounded = Round[corr, .01]

WeightedAdjacencyGraph[rounded,
 DirectedEdges -> True,
 EdgeStyle -> {DirectedEdge[i_, j_] :> AbsoluteThickness[rounded[[i, j]]]},
 EdgeLabels -> "EdgeWeight",
 PlotTheme -> "Scientific"]

3164plot.png
3164plot.png450Ă—392 17.5 KB

9

Hi Rohit,

That is great.

I noticed that recently in the scientific papers, researchers show the correlation between some lists through a graph like the following figure. I thought it may be interesting for you.

123.jpg
123.jpg815Ă—713 182 KB

Best Regards

Mohammad