topobench.transforms.liftings.graph2cell package

Submodules

topobench.transforms.liftings.graph2cell.base module

Abstract class for lifting graphs to cell complexes.

class topobench.transforms.liftings.graph2cell.base.Graph2CellLifting(complex_dim=2, **kwargs)

Bases: GraphLifting

Abstract class for lifting graphs to cell complexes.

Parameters:

complex_dimint, optional

The dimension of the cell complex to be generated. Default is 2.

**kwargsoptional

Additional arguments for the class.

topobench.transforms.liftings.graph2cell.cycle_lifting module

This module implements the cycle lifting for graphs to cell complexes.

class topobench.transforms.liftings.graph2cell.cycle_lifting.CellCycleLifting(max_cell_length=None, **kwargs)

Bases: Graph2CellLifting

Lift graphs to cell complexes.

The algorithm creates 2-cells by identifying the cycles and considering them as 2-cells.

Parameters:

max_cell_lengthint, optional

The maximum length of the cycles to be lifted. Default is None.

**kwargsoptional

Additional arguments for the class.

lift_topology(data: Data) → dict

Find the cycles of a graph and lifts them to 2-cells.

Parameters:

datatorch_geometric.data.Data

The input data to be lifted.

Returns:

dict

The lifted topology.

topobench.transforms.liftings.graph2cell.discrete_configuration_complex_lifting module

This module implements the discrete configuratio complex lifting lifting for graphs to cell complexes.

class topobench.transforms.liftings.graph2cell.discrete_configuration_complex_lifting.DiscreteConfigurationComplexLifting(k: int, preserve_edge_attr: bool = True, feature_aggregation='concat', **kwargs)

Bases: Graph2CellLifting

Lift graphs to cell complexes.

Lift graphs to cell complexes by generating the k-th discrete configuration complex D_k(G) of the graph. This is a cube complex, which is similar to a simplicial complex except each n-dimensional cell is homeomorphic to a n-dimensional cube rather than an n-dimensional simplex.

The discrete configuration complex of order k consists of all sets of k unique edges or vertices of G, with the additional constraint that if an edge e is in a cell, then neither of the endpoints of e are in the cell. For examples of different graphs and their configuration complexes, see the tutorial.

Note that since TopoNetx only supports cell complexes of dimension 2, if you generate a configuration complex of order k > 2 this will only produce the 2-skeleton.

Parameters:

kint

The order of the configuration complex, i.e. the number of ‘agents’ in a single configuration.

preserve_edge_attrbool, optional

Whether to preserve edge attributes. Default is True.

feature_aggregationstr, optional

For a k-agent configuration, the method by which the features are aggregated. Can be “mean”, “sum”, or “concat”. Default is “concat”.

**kwargsdict, optional

Additional arguments for the class.

Notes

The discrete configuration complex provides a way to model higher-order interactions in graphs, particularly useful for scenarios involving multiple agents or particles moving on a graph structure.

forward(data: Data) → Data

Apply the full lifting (topology + features) to the input data.

Parameters:

datatorch_geometric.data.Data

The input data to be lifted.

Returns:

torch_geometric.data.Data

The lifted data.

lift_topology(data: Data) → dict

Generate the cubical complex of discrete graph configurations.

Parameters:

datatorch_geometric.data.Data

The input data to be lifted.

Returns:

dict

The lifted topology.

topobench.transforms.liftings.graph2cell.discrete_configuration_complex_lifting.edge_cycle_to_vertex_cycle(edge_cycle: list[list | tuple])

Take a cycle represented by a list of edges and returns a vertex representation: [(1, 2), (0, 1), (1, 2)] -> [1, 2, 3].

Parameters:

edge_cyclelist[list | tuple]

The cycle represented by a list of edges.

Returns:

list

The cycle represented by a list of vertices.

topobench.transforms.liftings.graph2cell.discrete_configuration_complex_lifting.generate_configuration_class(graph: Graph, feature_aggregation: str, edge_features: bool)

Factory for the Configuration class.

Parameters:

graphnx.Graph

The input graph.

feature_aggregationstr

The method by which the features are aggregated.

edge_featuresbool

Whether edge features are present.

Returns:

Configuration

The Configuration.

Module contents

Graph2Cell liftings with automated exports.

class topobench.transforms.liftings.graph2cell.CellCycleLifting(max_cell_length=None, **kwargs)

Bases: Graph2CellLifting

Lift graphs to cell complexes.

The algorithm creates 2-cells by identifying the cycles and considering them as 2-cells.

Parameters:

max_cell_lengthint, optional

The maximum length of the cycles to be lifted. Default is None.

**kwargsoptional

Additional arguments for the class.

lift_topology(data: Data) → dict

Find the cycles of a graph and lifts them to 2-cells.

Parameters:

datatorch_geometric.data.Data

The input data to be lifted.

Returns:

dict

The lifted topology.

class topobench.transforms.liftings.graph2cell.DiscreteConfigurationComplexLifting(k: int, preserve_edge_attr: bool = True, feature_aggregation='concat', **kwargs)

Bases: Graph2CellLifting

Lift graphs to cell complexes.

Lift graphs to cell complexes by generating the k-th discrete configuration complex D_k(G) of the graph. This is a cube complex, which is similar to a simplicial complex except each n-dimensional cell is homeomorphic to a n-dimensional cube rather than an n-dimensional simplex.

The discrete configuration complex of order k consists of all sets of k unique edges or vertices of G, with the additional constraint that if an edge e is in a cell, then neither of the endpoints of e are in the cell. For examples of different graphs and their configuration complexes, see the tutorial.

Note that since TopoNetx only supports cell complexes of dimension 2, if you generate a configuration complex of order k > 2 this will only produce the 2-skeleton.

Parameters:

kint

The order of the configuration complex, i.e. the number of ‘agents’ in a single configuration.

preserve_edge_attrbool, optional

Whether to preserve edge attributes. Default is True.

feature_aggregationstr, optional

For a k-agent configuration, the method by which the features are aggregated. Can be “mean”, “sum”, or “concat”. Default is “concat”.

**kwargsdict, optional

Additional arguments for the class.

Notes

The discrete configuration complex provides a way to model higher-order interactions in graphs, particularly useful for scenarios involving multiple agents or particles moving on a graph structure.

forward(data: Data) → Data

Apply the full lifting (topology + features) to the input data.

Parameters:

datatorch_geometric.data.Data

The input data to be lifted.

Returns:

torch_geometric.data.Data

The lifted data.

lift_topology(data: Data) → dict

Generate the cubical complex of discrete graph configurations.

Parameters:

datatorch_geometric.data.Data

The input data to be lifted.

Returns:

dict

The lifted topology.

class topobench.transforms.liftings.graph2cell.Graph2CellLifting(complex_dim=2, **kwargs)

Bases: GraphLifting

Abstract class for lifting graphs to cell complexes.

Parameters:

complex_dimint, optional

The dimension of the cell complex to be generated. Default is 2.

**kwargsoptional

Additional arguments for the class.