1.4. MapperGraph class

This is the mapper graph class which is inherited from the Reeb graph class. The main differences are

1. The Mapper graph is a graph with a function, but all function values are stored as integers. There is also a stored delta value which is can be used for scaling, so that all function values can be thought of as delta * f(v).

2. All edges have adjacent integer values. This equivalently means that no integer has a point in the interior of an edge in its inverse image.

Note that this class can be imported as:

import cereeberus
R = cereeberus.MapperGraph()

class cereeberus.reeb.mapper.MapperGraph(G=None, f={}, delta=None, seed=None, verbose=False)

A mapper graph structure. This inherits the properties of the Reeb graph in that it is a graph with a function given on the vertices, but with some additional requirements.

• The values are integers in some range, [n_low, n_low+1, cdots, n_high], although we consider the funciton values to be [delta * n_low, delta* (n_low+1), cdots, delta * n_high] for a stored delta

• If an edge crosses a value, it has a vertex (so that the inverse image of any integer is only vertices, not interiors of edges)

• An internal delta is stored so that this can be interpreted as function values [delta * n_low, delta* (n_low+1), cdots, delta * n_high]

__init__(G=None, f={}, delta=None, seed=None, verbose=False)

Initializes a Reeb graph object.

Parameters:

• G – nx.graph, optional. If not None, a graph to initialize the Reeb graph.

• f – dict, optional. If not an empty dictionary, a dictionary of function values associated with the graph nodes.

• seed – int, optional. If not None, a seed to pass to the spring layout.

• verbose – bool, optional. If True, will print out additional information during initialization.

add_edge(u, v, reset_pos=True)

Add an edge to the graph. This will also update the internal structure to make sure it satisfies the mapper properties.

mapperify()

Take the internal structure and make sure it satisfies the requirement that all edges have adjacent function values.

add_node(vertex, f_vertex, reset_pos=True)

Same as adding a node in Reeb, but with the additional requirement that the function value is an integer.

set_pos_from_f(seed=None, verbose=False)

Same as the Reeb graph function, but we want to draw the vertex locations at delta*function value.

induced_subgraph(nodes)

Returns the subgraph of the mapper graph induced by the nodes in the list nodes.

Parameters:

nodes (list) – The list of nodes to include in the subgraph.

Returns:

MapperGraph