5. Example graphs

In this notebook, we show the available example graphs from the data module.

5.1. Reeb graphs

These cells generate the examples from the example Reeb graphs module.

import cereeberus.data.ex_reebgraphs as ex_rg
import matplotlib.pyplot as plt

# The torus graph allows for choices of function values for the four vertices
R = ex_rg.line(a = 0, b = 3)
R.draw()
plt.title('Line graph')

plt.savefig('../images/line.png', bbox_inches = 'tight')

# The torus graph allows for choices of function values for the four vertices
R = ex_rg.torus(a = 0, b = 2, c = 4, d = 5,
                multigraph = True, seed = 6)
R.draw(cpx = 3)
plt.title('Torus graph - Multigraph')

# plt.savefig('../images/torus.png', bbox_inches = 'tight')

Text(0.5, 1.0, 'Torus graph - Multigraph')

# The torus graph allows for choices of function values for the four vertices
R = ex_rg.torus(a = 0, b = 1, c = 4, d = 5,
                multigraph = False, seed = 6)
R.draw(cpx = 3, with_labels = False)
plt.title('Torus graph - Non-multigraph')

plt.savefig('../images/torus-extraverts.png', bbox_inches = 'tight')

R = ex_rg.dancing_man(seed = 0)
R.draw(with_labels = False)
plt.title('Dancing Man')
# plt.savefig('../images/dancing_man.png', bbox_inches = 'tight')

Text(0.5, 1.0, 'Dancing Man')

R = ex_rg.juggling_man(seed = 0)
R.draw(with_labels = False)
plt.title('Juggling Man')

# plt.savefig('../images/juggling_man.png', bbox_inches = 'tight')

Text(0.5, 1.0, 'Juggling Man')

R = ex_rg.simple_loops(seed = 5)

R.draw(with_labels = False, cpx= 1.1)
plt.title('Simple loops')

# plt.savefig('../images/simple_loops.png', bbox_inches = 'tight')

Text(0.5, 1.0, 'Simple loops')

R = ex_rg.interleave_example_A(seed = 5)

R.draw(with_labels = False, cpx= 1.1)
plt.title('Interleaving example A')

# plt.savefig('../images/interleave_example_A.png', bbox_inches = 'tight')

Text(0.5, 1.0, 'Interleaving example A')

R = ex_rg.interleave_example_B(seed = 5)

R.draw(with_labels = False, cpx= 1.1)
plt.title('Interleaving example B')

# plt.savefig('../images/interleave_example_B.png', bbox_inches = 'tight')

Text(0.5, 1.0, 'Interleaving example B')

5.2. Mapper Graphs

These cells generate the examples from the example mapper graphs module.

import cereeberus.data.ex_mappergraphs as ex_mg
import matplotlib.pyplot as plt

# The line graph allows for choices of function values for the bottom and top vertices
MG = ex_mg.line(a = 0, b = 3)
MG.draw(with_labels = False)
plt.title('Line graph - Mapper')

# plt.savefig('../images/line_mapper.png', bbox_inches = 'tight')

# Note that like the Reeb graph version, the torus mapper graph allows for choices of integer function values for the four vertices
MG = ex_mg.torus(a = 0, b = 1, c = 4, d = 6, delta = .2, seed = 5)

print(f"Delta value is: {MG.delta}")

MG.draw()
plt.title('Torus graph mapper')

# plt.savefig('torus_mapper.png', bbox_inches = 'tight')

Delta value is: 0.2

Text(0.5, 1.0, 'Torus graph mapper')

MG = ex_mg.dancing_man(seed = 2)
print(f"Delta value is: {MG.delta}")
MG.draw(with_labels = False)
plt.title('Dancing Man Mapper')
# plt.savefig('dancing_man_mapper.png', bbox_inches = 'tight')

Delta value is: 0.1

Text(0.5, 1.0, 'Dancing Man Mapper')

MG = ex_mg.juggling_man(seed = 0)
print(f"Delta value is: {MG.delta}")

MG.draw(with_labels = False)
plt.title('Juggling Man Mapper')

# plt.savefig('juggling_man_mapper.png', bbox_inches = 'tight')

Delta value is: 0.1

Text(0.5, 1.0, 'Juggling Man Mapper')

MG = ex_mg.simple_loops(seed = 5)
print(f"Delta value is: {MG.delta}")

MG.draw(with_labels = False, cpx= 1.1)
plt.title('Simple loops mapper')

# plt.savefig('simple_loops_mapper.png', bbox_inches = 'tight')

Delta value is: 1

Text(0.5, 1.0, 'Simple loops mapper')

MG = ex_mg.interleave_example_A(seed = 5)
print(f"Delta value is: {MG.delta}")

MG.draw(with_labels = False)
plt.title('Interleaving example A mapper')

# plt.savefig('interleave_example_A_mapper.png', bbox_inches = 'tight')

Delta value is: 1

Text(0.5, 1.0, 'Interleaving example A mapper')

MG = ex_mg.interleave_example_B(seed = 5)
print(f"Delta value is: {MG.delta}")

MG.draw(with_labels = False)
plt.title('Interleaving example B mapper')

# plt.savefig('interleave_example_B_mapper.png', bbox_inches = 'tight')

Delta value is: 1

Text(0.5, 1.0, 'Interleaving example B mapper')

5.3. Merge Trees

TODO

5.4. Embedded Graphs

TODO