scott.topology.ph

class scott.topology.ph.GraphHomology(homology_dims: List[int] | None = None, filter_attribute: str = 'curvature', mask_infinite_features: bool = False, extended_persistence: bool = True)

Bases: object

Compute persistent homology on graphs by filtering over edge attributes.

This class uses Gudhi’s SimplexTree to build a clique complex on a given graph and compute persistence diagrams for homology groups, using an edge attribute (e.g. curvature) as a filtration function.

homology_dims

Dimensions of the homology groups to compute (e.g., [0, 1] for H_0 and H_1). Default is [0, 1].

Type:

List[int]

filter_attribute

The edge attribute to use as the filtration value. Default is “curvature”.

Type:

str, optional

__init__(homology_dims: List[int] | None = None, filter_attribute: str = 'curvature', mask_infinite_features: bool = False, extended_persistence: bool = True)

Initializes the GraphHomology class with parameters for homology computation.

Parameters:

• homology_dims (list of int, optional) – Dimensions of the homology groups to compute (e.g., [0, 1] for H_0 and H_1). Default is [0, 1].

• filter_attribute (str, optional) – The edge attribute to use as the filtration value. Default is “curvature”.

calculate_persistent_homology(G: Graph) → PersistenceDiagram

Calculates persistent homology of the graph’s clique complex.

Parameters:

G (networkx.Graph) – Input graph with edges that contain attributes for filtration.

Returns:

A persistence diagram wrapper for the topological information from a curvature filtration. Attribute persistence_pts stores a Dict[int, np.array] that a maps homology dimension key to a np.array of its persistence pairs.

Return type:

PersistenceDiagram

Raises:

ValueError – If the specified filter_attribute is not found in an edge’s attributes.