1.3. Embedded Graphs

This is the Embedded graph class which inherits structure from nx.Graph.

Note that this class can be imported as:

import cereeberus
T = cereeberus.EmbeddedGraph()

class cereeberus.reeb.embeddedgraph.EmbeddedGraph[source]

A class to represent a graph with 2D embedded coordinates for each vertex.

Attributes

graphnx.Graph: a NetworkX graph object
coordinatesdict: a dictionary mapping vertices to their (x, y) coordinates

__init__()[source]: Initializes an empty EmbeddedGraph object.

add_node(vertex, x, y)[source]

Adds a vertex to the graph and assigns it the given coordinates.

Parameters:

vertex (str) – The vertex to be added.
x (float) – The x-coordinate of the vertex.
y (float) – The y-coordinate of the vertex.

add_nodes_from(nodes, coordinates)[source]

Adds multiple vertices to the graph and assigns them the given coordinates.

Parameters:

nodes (list) – A list of vertices to be added.
coordinates (dict) – A dictionary mapping vertices to their coordinates.

add_edge(u, v)[source]

Adds an edge between the vertices u and v if they exist.

Parameters:

u (str) – The first vertex of the edge.
v (str) – The second vertex of the edge.

get_coordinates(vertex)[source]

Returns the coordinates of the given vertex.

Parameters:: vertex (str) – The vertex whose coordinates are to be returned.
Returns:: The coordinates of the vertex.
Return type:: tuple

set_coordinates(vertex, x, y)[source]

Sets the coordinates of the given vertex.

Parameters:

vertex (str) – The vertex whose coordinates are to be set.
x (float) – The new x-coordinate of the vertex.
y (float) – The new y-coordinate of the vertex.

Raises:

ValueError – If the vertex does not exist in the graph.

get_bounding_box()[source]

Method to find a bounding box of the vertex coordinates in the graph.

Returns:: A list of tuples representing the minimum and maximum x and y coordinates.
Return type:: list

get_bounding_radius()[source]

Method to find the radius of the bounding circle of the vertex coordinates in the graph.

Returns:: The radius of the bounding circle.
Return type:: float

get_mean_centered_coordinates()[source]

Method to find the mean-centered coordinates of the vertices in the graph.

Returns:: A dictionary mapping vertices to their mean-centered coordinates.
Return type:: dict

set_mean_centered_coordinates()[source]: Method to set the mean-centered coordinates of the vertices in the graph. Warning: This overwrites the original coordinates

g_omega(theta)[source]

Function to compute the function \(g_\omega(v)\) for all vertices \(v\) in the graph in the direction of \(\theta \in [0,2\pi]\) . This function is defined by \(g_\omega(v) = \langle \texttt{pos}(v), \omega \rangle\) .

Parameters:: theta (float) – The angle in \([0,2\pi]\) for the direction to compute the \(g(v)\) values.
Returns:: A dictionary mapping vertices to their \(g(v)\) values.
Return type:: dict

g_omega_edges(theta)[source]

Calculates the function value of the edges of the graph by making the value equal to the max vertex value

Parameters:

theta (float) – The direction of the function to be calculated.

Returns:

dict: A dictionary of the function values of the edges.

sort_vertices(theta, return_g=False)[source]

Function to sort the vertices of the graph according to the function g_omega(v) in the direction of theta in [0,2*np.pi].

Parameters:

theta (float) – The angle in [0,2*np.pi] for the direction to sort the vertices.
return_g (bool) – Whether to return the g(v) values along with the sorted vertices.

Returns:

list: A list of vertices sorted in increasing order of the \(g(v)\) values. If return_g is True, also returns the g dictionary with the function values g[vertex_name]=func_value.

sort_edges(theta, return_g=False)[source]

Function to sort the edges of the graph according to the function

\[g_\omega(e) = \max \{ g_\omega(v) \mid v \in e \}\]

in the direction of \(\theta \in [0,2\pi]\) .

Parameters:

theta (float) – The angle in \([0,2\pi]\) for the direction to sort the edges.
return_g (bool) – Whether to return the \(g(v)\) values along with the sorted edges.

Returns:

A list of edges sorted in increasing order of the \(g(v)\) values. If return_g is True, also returns the g dictionary with the function values g[vertex_name]=func_value.

lower_edges(v, omega)[source]

Function to compute the number of lower edges of a vertex v for a specific direction (included by the use of sorted v_list).

Parameters:

v (str) – The vertex to compute the number of lower edges for.
omega (tuple) – The direction vector to consider given as an angle in [0, 2pi].

Returns:

The number of lower edges of the vertex v.

Return type:

int

plot(bounding_circle=False, color_nodes_theta=None, ax=None, **kwargs)[source]

Function to plot the graph with the embedded coordinates.

If bounding_circle is True, a bounding circle is drawn around the graph.

If color_nodes_theta is not None, it should be given as a theta in \([0,2\pi]\). Then the nodes are colored according to the \(g(v)\) values in the direction of theta.

reeb_graph_from_direction(theta)[source]

Function to create a ReebGraph from a given direction theta.

Parameters:: theta (float) – The direction in [0, 2pi] to calculate the ReebGraph.
Returns:: The ReebGraph object created from the EmbeddedGraph.
Return type:: ReebGraph