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 AlignmentClusterPlot

Source Notebook

Generate a density plot of opinion alignment from a list of relations

Contributed by: William Choi-Kim

ResourceFunction["AlignmentClusterPlot"][relations]

generates a density plot based on the relationships in relations.

Details and Options

relations is a list or association of index pairs and agreement factors. This is an array of two indices for each key and a relationship factor (a real number where negative is disagreement and positive is agreement) for each value or a list of such associations.
The option Steps→steps (default 100) generates a density plot after running the alignment simulation steps times. It must be set to a positive integer, and best results are obtained when steps >= 100.
The resulting plot is a heatmap of agreement and disagreement in a community, where individuals that agree clump together in high-density areas. If a list of associations was provided the heatmap is two dimensional and visualizes each association starting from the bottom and going upward.

Examples

Basic Examples (2) 

Plot the alignment of 5 individuals:

In[1]:=
data = <|{1, 2} -> 0.6, {1, 3} -> 0.6, {1, 4} -> -1., {1, 5} -> -0.6, {2, 3} -> -0.2, {2, 4} -> 0.6, {2, 5} -> 1., {3, 4} -> 0.6, {3, 5} -> 0.2, {4, 5} -> -0.6|>;
In[2]:=
ResourceFunction["AlignmentClusterPlot"][data]
Out[2]=

Plot the alignment of 30 individuals over ten time points:

In[3]:=
(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/00ad4143-a744-44db-b252-a93068a69781"]
In[4]:=
ResourceFunction["AlignmentClusterPlot"][matrix]
Out[4]=

Scope (1) 

Steps (1) 

Each alignment plot is generated by stepping each individual in either direction until the forces (attraction for agreement and repulsion for disagreement) are balanced. Increasing the number of steps improves the accuracy of the plot, but returns diminish as steps increases:

In[5]:=
data = <|{1, 2} -> 0.6, {1, 3} -> 0.6, {1, 4} -> -1., {1, 5} -> -0.6, {2, 3} -> -0.2, {2, 4} -> 0.6, {2, 5} -> 1., {3, 4} -> 0.6, {3, 5} -> 0.2, {4, 5} -> -0.6|>; ResourceFunction["AlignmentClusterPlot"][data, Steps -> #] & /@ Range[10]
Out[6]=

Possible Issues (1) 

Particularly volatile data can lead to artifacts in the plot:

In[7]:=
data = <|{1, 2} -> -0.2, {1, 3} -> 0.2, {1, 4} -> 0.2, {1, 5} -> 0.2, {1, 6} -> 0.2, {1, 7} -> 0.2, {1, 8} -> -0.2, {1, 9} -> 0.2, {1, 10} -> 0.2, {2, 3} -> -0.6, {2, 4} -> 0.2, {2, 5} -> -0.6, {2, 6} -> 0.2, {2, 7} -> 0.2, {2, 8} -> 0.6, {2, 9} -> 1., {2, 10} -> 0.2, {3, 4} -> 0.6, {3, 5} -> -0.2, {3, 6} -> 0.6, {3, 7} -> -0.2, {3, 8} -> 0.2, {3, 9} -> 0.6, {3, 10} -> -0.2, {4, 5} -> -0.2, {4, 6} -> -1., {4, 7} -> 0.6, {4, 8} -> 0.2, {4, 9} -> -0.2, {4, 10} -> 0.6, {5, 6} -> -0.2, {5, 7} -> -0.2, {5, 8} -> 1., {5, 9} -> 0.6, {5, 10} -> 0.6, {6, 7} -> 0.6, {6, 8} -> 0.2, {6, 9} -> -0.2, {6, 10} -> 0.6, {7, 8} -> 0.2, {7, 9} -> -0.2, {7, 10} -> -0.2, {8, 9} -> -0.6, {8, 10} -> -0.6, {9, 10} -> -0.2|>; ResourceFunction["AlignmentClusterPlot"][data, Steps -> 10]
Out[12]=

Neat Examples (1) 

Visualize the level of agreement in the voting record of 50 members of Congress on four particular votes:

In[13]:=
(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/5ebf0827-1113-43bb-aaa5-7b3459640a52"]
Out[14]=

Publisher

William Choi-Kim

Requirements

Wolfram Language 13.0 (December 2021) or above

Version History

  • 1.0.0 – 10 July 2025

Related Resources

License Information