core.figure_generation_files package

Submodules

core.figure_generation_files.pathmarker module

class core.figure_generation_files.pathmarker.PathMarker(graph, pos, default_edges, default_nodes)[source]

Bases: object

A class that represents a path marker for a graph. This is used as a class since we want to keep track of one instance of a graph. This instance is used to keep track of the marked nodes and edges in the graph. Note we can mark nodes with left-click and right-click. Marked nodes and edges are drawn in royalblue color, while right-click marked nodes are drawn in darkturquoise color.

Note

  • Both nodes and edges can be marked with left-click.

  • Only nodes can be right-click marked. Edges cannot!

graph

The networkx graph object.

Type:

nx.Graph

pos

The position of the nodes in the graph. The keys are the nodes and the values are the positions.

Type:

dict

marked_nodes

A set of marked nodes. Starts empty.

Type:

set

right_marked_nodes

A set of right-click marked nodes. Starts empty.

Type:

set

marked_edges

A set of marked edges. Starts empty.

Type:

set

edge_colors

A list of colors for the edges. Is black by default. If a Lehmer path is highlighted, the edge colors are changed to red.

Type:

list

node_colors

A list of colors for the nodes. Is lightblue by default. If a Lehmer path is highlighted, the graph has the following colors:

  • Orange for the spur bases

  • Olive for the spur tips

  • Deeppink for the other visited nodes

  • Lightblue for the unvisited nodes

Type:

list

mark_node(node)[source]

Marks a node.

Parameters:

node (str) – The node to be marked.

Return type:

None

Returns:

None

right_mark_node(node)[source]

Marks a node with a right-click.

Parameters:

node (str) – The node to be right-click marked.

Return type:

None

Returns:

None

un_right_mark_node(node)[source]

Unmarks a right-click marked node.

Parameters:

node (str) – The node to be unmarked.

Return type:

None

Returns:

None

unmark_node(node)[source]

Unmarks a node.

Parameters:

node (str) – The node to be unmarked.

Return type:

None

Returns:

None

toggle_node(node)[source]

Toggles the marking of a node.

Parameters:

node (str) – The node to be toggled.

Return type:

None

Returns:

None

toggle_right_mark_node(node)[source]

Toggles the right-click marking of a node. If the node is already right-click marked, it will be unmarked and vice versa.

Parameters:

node (str) – The node to be toggled.

Return type:

None

Returns:

None

mark_edge(edge)[source]

Marks an edge.

Parameters:

edge (tuple[str, str]) – The edge to be marked.

Return type:

None

Returns:

None

unmark_edge(edge)[source]

Unmarks an edge.

Parameters:

edge (tuple[str, str]) – The edge to be unmarked.

Return type:

None

Returns:

None

toggle_edge(edge)[source]

Toggles the marking of an edge. If the edge is already marked, it will be unmarked and vice versa.

Parameters:

edge (tuple[str, str]) – The edge to be toggled.

Return type:

None

Returns:

None

reset_colors()[source]

Clears the sets of marked nodes and edges. This is to reset the colors of the graph.

Return type:

None

Returns:

None

update_plot(nx, plt_instance)[source]

Updates the plot with the marked nodes and edges. Draws it in the matplotlib pyplot instance. Marked nodes and edges are drawn in royalblue color. For right-click marked nodes, they are drawn in darkturquoise color.

Parameters:

  • nx (nx.Graph) – The networkx graph object.

  • plt_instance (plt) – The matplotlib pyplot instance.

Return type:

None

Returns:

None

core.figure_generation_files.rivertz module

core.figure_generation_files.rivertz.swap_elements(a_list, i, j)[source]

Swaps the elements at positions i and j in the given list.

Parameters:

  • a_list (list) – The list in which the elements will be swapped.

  • i (int) – The index of the first element to be swapped.

  • j (int) – The index of the second element to be swapped.

Returns:

(the list is modified in place)

Return type:

None

class core.figure_generation_files.rivertz.SetPerm(multiplicity)[source]

Bases: Iterator, ABC

This file is directly copied from the original source code of the article: “Multiset permutation generation by transpositions” by Rivertz The original source code is available at: https://doi.org/10.48550/arXiv.2309.11781

Therefore we also did not test or document this file as it is not part of our codebase.

References

  • Hans Jakob Rivertz. Multiset permutation generation by transpositions. 9 2023

swap(i, j, df)[source]
one_step(n)[source]

core.figure_generation_files.verhoeffCycleCoverPaths module

core.figure_generation_files.verhoeffCycleCoverPaths.fig11(ax, even_int)[source]

Generate and plot Figure 11 from Verhoeff’s paper (see References). The figure displays a path between c and d:

  • c1 = 12 0^k_0 1

  • d1 = 0 21 0^{k_0-1} 1

where k_0 is an even integer (even_int). The path is highlighted in blue and important nodes are marked.

Parameters:

  • ax (Axes) – The matplotlib Axes object to plot the figure on.

  • even_int (int) – An even integer value.

Returns:

Works in place to plot the figure on the given ax.

Return type:

None

References

  • Tom Verhoeff. The spurs of D. H. Lehmer: Hamiltonian paths in neighbor-swap graphs of permutations. Designs, Codes, and Cryptography, 84(1-2):295-310, 7 2017.

core.figure_generation_files.verhoeffCycleCoverPaths.fig12(ax, even_int)[source]

Generate and plot Figure 12 from Verhoeff’s paper (see References). The figure displays a path between a and b:

  • a0 = 12 0^{k_0-1} 1 0

  • b0 = 0 21 0^{k_0-2} 1 0

where k_0 is an even integer (even_int). The path is highlighted in blue and important nodes are marked.

Parameters:

  • ax (Axes) – The matplotlib Axes object to plot the figure on.

  • even_int (int) – An even integer value.

Returns:

Works in place to plot the figure on the given ax.

Return type:

None

References

  • Tom Verhoeff. The spurs of D. H. Lehmer: Hamiltonian paths in neighbor-swap graphs of permutations. Designs, Codes, and Cryptography, 84(1-2):295-310, 7 2017.

core.figure_generation_files.verhoeffCycleCoverPaths.fig12_e_f(ax, even_int)[source]

Generate and plot Figure 12 from Verhoeff’s paper (see References). The figure displays a path between e and f:

  • e0 = 1 02 0^{k_0-2} 1 0

  • f0 = 0 12 0^{k_0-2} 1 0

where k_0 is an even integer (even_int). The path is highlighted in blue and important nodes are marked.

Parameters:

  • ax (Axes) – The matplotlib Axes object to plot the figure on.

  • even_int (int) – An even integer value.

Returns:

Works in place to plot the figure on the given ax.

Return type:

None

References

  • Tom Verhoeff. The spurs of D. H. Lehmer: Hamiltonian paths in neighbor-swap graphs of permutations. Designs, Codes, and Cryptography, 84(1-2):295-310, 7 2017.

core.figure_generation_files.verhoeffCycleCoverPaths.combined_figure(even_int, save=False)[source]

Generate and plot both Figure 11 and Figure 12 from Verhoeff’s paper (see References) in a single plot. The figures display paths between c and d and between a and b respectively. The paths are highlighted in blue and important nodes are marked.

Parameters:

  • even_int (int) – An even integer value.

  • save (bool, optional) – Save the image in the ./out directory.

Returns:

Works in place to plot the figure.

Return type:

None

References

  • Tom Verhoeff. The spurs of D. H. Lehmer: Hamiltonian paths in neighbor-swap graphs of permutations. Designs, Codes, and Cryptography, 84(1-2):295-310, 7 2017.

core.figure_generation_files.verhoeffCycleCoverPaths.plot_individual_figures(even_int, save=False, cycle=False)[source]

Generate and plot Figure 11 and Figure 12 from Verhoeff’s paper (see References) in separate plots. The figures display paths between c and d and between a and b respectively. The paths are highlighted in blue and important nodes are marked. If save is enabled, the images are saved in the ./out directory. If not, the figures are displayed.

Parameters:

  • even_int (int) – An even integer value, the number of 0s in the signature.

  • save (bool, optional) – Save the images in the ./out directory. Defaults to False which displays the figures.

  • cycle (bool, optional) – Generate a cycle instead of a path. Default is False.

Returns:

Works in place to plot the figures.

Return type:

None

References

  • Tom Verhoeff. The spurs of D. H. Lehmer: Hamiltonian paths in neighbor-swap graphs of permutations. Designs, Codes, and Cryptography, 84(1-2):295-310, 7 2017.

Module contents