Venn diagram plotting routines for Python/Matplotlib

Routines for plotting area-weighted two- and three-circle venn diagrams.

Installation

Install the package as usual via pip:

$ python -m pip install matplotlib-venn

Since version 1.1.0 the package includes an extra "cost based" layout algorithm for venn3 diagrams, that relies on the shapely package, which is not installed as a default dependency. If you need the new algorithm (or just have nothing against installing shapely along the way), instead do:

$ python -m pip install "matplotlib-venn[shapely]"

It is quite probable that shapely will become a required dependency eventually in one of the future versions.

Dependencies

• numpy,
• scipy,
• matplotlib,
• shapely (optional).

Usage

The package provides four main functions: venn2, venn2_circles, venn3 and venn3_circles.

The functions venn2 and venn2_circles accept as their only required argument a 3-element tuple (Ab, aB, AB) of subset sizes, and draw a two-circle venn diagram with respective region areas, e.g.:

venn2(subsets = (3, 2, 1))

In this example, the region, corresponding to subset A and not B will be three times larger in area than the region, corresponding to subset A and B.

You can also provide a tuple of two set or Counter (i.e. multi-set) objects instead (new in version 0.7), e.g.:

venn2((set(['A', 'B', 'C', 'D']), set(['D', 'E', 'F'])))

Similarly, the functions venn3 and venn3_circles take a 7-element tuple of subset sizes (Abc, aBc, ABc, abC, AbC, aBC, ABC), and draw a three-circle area-weighted Venn diagram:

Alternatively, a tuple of three set or Counter objects may be provided.

The functions venn2 and venn3 draw the diagrams as a collection of colored patches, annotated with text labels. The functions venn2_circles and venn3_circles draw just the circles.

The functions venn2_circles and venn3_circles return the list of matplotlib.patch.Circle objects that may be tuned further to your liking. The functions venn2 and venn3 return an object of class VennDiagram, which gives access to constituent patches, text elements, and (since version 0.7) the information about the centers and radii of the circles.

Basic Example:

from matplotlib_venn import venn2
venn2(subsets = (3, 2, 1))

For the three-circle case:

from matplotlib_venn import venn3
venn3(subsets = (1, 1, 1, 2, 1, 2, 2), set_labels = ('Set1', 'Set2', 'Set3'))

A more elaborate example:

from matplotlib import pyplot as plt
import numpy as np
from matplotlib_venn import venn3, venn3_circles
plt.figure(figsize=(4,4))
v = venn3(subsets=(1, 1, 1, 1, 1, 1, 1), set_labels = ('A', 'B', 'C'))
v.get_patch_by_id('100').set_alpha(1.0)
v.get_patch_by_id('100').set_color('white')
v.get_label_by_id('100').set_text('Unknown')
v.get_label_by_id('A').set_text('Set "A"')
c = venn3_circles(subsets=(1, 1, 1, 1, 1, 1, 1), linestyle='dashed')
c[0].set_lw(1.0)
c[0].set_ls('dotted')
plt.title("Sample Venn diagram")
plt.annotate('Unknown set', xy=v.get_label_by_id('100').get_position() - np.array([0, 0.05]), xytext=(-70,-70),
             ha='center', textcoords='offset points', bbox=dict(boxstyle='round,pad=0.5', fc='gray', alpha=0.1),
             arrowprops=dict(arrowstyle='->', connectionstyle='arc3,rad=0.5',color='gray'))
plt.show()

An example with multiple subplots:

from matplotlib_venn import venn2, venn2_circles
figure, axes = plt.subplots(2, 2)
venn2(subsets={'10': 1, '01': 1, '11': 1}, set_labels = ('A', 'B'), ax=axes[0][0])
venn2_circles((1, 2, 3), ax=axes[0][1])
venn3(subsets=(1, 1, 1, 1, 1, 1, 1), set_labels = ('A', 'B', 'C'), ax=axes[1][0])
venn3_circles({'001': 10, '100': 20, '010': 21, '110': 13, '011': 14}, ax=axes[1][1])
plt.show()

Perhaps the most common use case is generating a Venn diagram given three sets of objects:

set1 = set(['A', 'B', 'C', 'D'])
set2 = set(['B', 'C', 'D', 'E'])
set3 = set(['C', 'D',' E', 'F', 'G'])

venn3([set1, set2, set3], ('Set1', 'Set2', 'Set3'))
plt.show()

Tuning the diagram layout

Note that for a three-circle venn diagram it is not in general possible to achieve exact correspondence between the required set sizes and region areas. The default layout algorithm aims to correctly represent:

• Relative areas of the full individual sets (A, B, C).
• Relative areas of pairwise intersections of sets (A&B, A&C, B&C, not to be confused with the regions A&B&~C, A&~B&C, ~A&B&C, on the diagram).

Sometimes the result is unsatisfactory and either the area weighting or the layout logic needs to be tuned.

The area weighing can be adjusted by providing a fixed_subset_sizes argument to the DefaultLayoutAlgorithm:

from matplotlib_venn.layout.venn2 import DefaultLayoutAlgorithm
venn2((1,2,3), layout_algorithm=DefaultLayoutAlgorithm(fixed_subset_sizes=(1,1,1)))

from matplotlib_venn.layout.venn3 import DefaultLayoutAlgorithm
venn3((7,6,5,4,3,2,1), layout_algorithm=DefaultLayoutAlgorithm(fixed_subset_sizes=(1,1,1,1,1,1,1)))

In the above examples the diagram regions will be plotted as if venn2((1,1,1)) and venn3((1,1,1,1,1,1,1)) were invoked, yet the actual numbers will be (1,2,3) and (7,6,5,4,3,2,1) respectively.

The diagram can be tuned further by switching the layout algorithm to a different implementation. At the moment the package offers an alternative layout algorithm for venn3 diagrams that lays the circles out by optimizing a user-provided cost function. The following examples illustrate its usage:

from matplotlib_venn.layout.venn3 import cost_based
subset_sizes = (100,200,10000,10,20,3,1)
venn3(subset_sizes, layout_algorithm=cost_based.LayoutAlgorithm())

alg = cost_based.LayoutAlgorithm(cost_fn=cost_based.WeightedAggregateCost(transform_fn=lambda x: x))
venn3(subset_sizes, layout_algorithm=alg)

alg = cost_based.LayoutAlgorithm(cost_fn=cost_based.WeightedAggregateCost(weights=(0,0,0,1,1,1,1)))
venn3(subset_sizes, layout_algorithm=alg)

The default "pairwise" algorithm is, theoretically, a special case of the cost-based method with the respective cost function:

alg = cost_based.LayoutAlgorithm(cost_fn=cost_based.pairwise_cost)
venn3(subset_sizes, layout_algorithm=alg)

(The latter plot will be close, but not perfectly equal to the outcome of DefaultLayoutAlgorithm()).

Note that the import:

from matplotlib_venn.layout.venn3 import cost_based

will fail unless you have the optional shapely package installed (see "Installation" above).

Questions

• If you ask your questions at StackOverflow and tag them matplotlib-venn, chances are high you could get an answer from the maintainer of this package.

See also

• Report issues and submit fixes at Github: https://github.com/konstantint/matplotlib-venn

  Check out the DEVELOPER-README.rst for development-related notes.

• Some alternative means of plotting a Venn diagram (as of October 2012) are reviewed in the blog post: http://fouryears.eu/2012/10/13/venn-diagrams-in-python/

• The matplotlib-subsets package visualizes a hierarchy of sets as a tree of rectangles.

• The matplotlib_set_diagrams package is a GPL-licensed alternative that offers a different layout algorithm, which supports more than three sets and provides a cool ability to incorporate wordclouds into your Venn (Euler) diagrams.