topobench.transforms.liftings.graph2simplicial package

Graph2SimplicialLifting module with automated exports.

class Graph2SimplicialLifting(complex_dim=2, **kwargs)

Bases: GraphLifting

Abstract class for lifting graphs to simplicial complexes.

Parameters:

complex_dimint, optional

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

**kwargsoptional

Additional arguments for the class.

__init__(complex_dim=2, **kwargs)

class LatentCliqueLifting(edge_prob_mean=0.9, edge_prob_var=0.05, it=20, init='edges', do_gibbs=False, **kwargs)

Bases: Graph2SimplicialLifting

Lift graphs to cell complexes by identifying the cycles as 2-cells.

Parameters:

edge_prob_meanfloat = 0.9

Mean of the prior distribution of pie ~ Beta where edge_prob_mean must be in (0, 1). When edge_prob_mean is one, the value of edge_prob is fixed and not sampled.

edge_prob_varfloat = 0.05

Uncertainty of the prior distribution of pie ~ Beta(a, b) where edge_prob_var must be in [0, inf). When edge_prob_var is zero, the value of edge_prob is fixed and not sampled. It is require dthat edge_prob_var < edge_prob_mean * (1 - edge_prob_mean). When this is not the case the value of edge_prob_var is set to edge_prob_mean * (1 - edge_prob_mean) - 1e-6.

itint, optional

Number of iterations for sampling, by default None.

initstr, optional

Initialization method for the clique cover matrix, by default “edges”.

do_gibbsbool, optional

Whether to perform Gibbs sampling, by default False.

**kwargsoptional

Additional arguments for the class.

__init__(edge_prob_mean=0.9, edge_prob_var=0.05, it=20, init='edges', do_gibbs=False, **kwargs)

lift_topology(data, verbose=True)

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

Parameters:

datatorch_geometric.data.Data

The input data to be lifted.

verbosebool, optional

Whether to display verbose output, by default False.

Returns:

dict

The lifted topology.

class NeighborhoodComplexLifting(max_simplices=10, **kwargs)

Bases: Graph2SimplicialLifting

Lifts graphs to a simplicial complex domain by identifying the neighborhood complex as k-simplices.

Parameters:

max_simplicesint, optional

The maximum number of simplices to be added to the simplicial complex for each node. Default is 50.

**kwargsoptional

Additional arguments for the class.

__init__(max_simplices=10, **kwargs)

lift_topology(data)

Lift the topology of a graph to a simplicial complex.

Parameters:

datatorch_geometric.data.Data

The input data to be lifted.

Returns:

dict

The lifted topology.

class SimplicialCliqueLifting(**kwargs)

Bases: Graph2SimplicialLifting

Lift graphs to simplicial complex domain.

The algorithm creates simplices by identifying the cliques and considering them as simplices of the same dimension.

Parameters:

**kwargsoptional

Additional arguments for the class.

__init__(**kwargs)

lift_topology(data)

Lift the topology of a graph to a simplicial complex.

Parameters:

datatorch_geometric.data.Data

The input data to be lifted.

Returns:

dict

The lifted topology.

class SimplicialDnDLifting(**kwargs)

Bases: Graph2SimplicialLifting

Lift graphs to simplicial complex domain using a Dungeons & Dragons inspired system.

Parameters:

**kwargsoptional

Additional arguments for the class.

__init__(**kwargs)

lift_topology(data, max_simplices=10)

Lift the topology of a graph to a simplicial complex using Dungeons & Dragons (D&D) inspired mechanics.

Parameters:

dataData

The input data to be lifted.

max_simplicesint

Maximum number of simplices to add for each node attribute.

Returns:

dict

The lifted topology.

class SimplicialEccentricityLifting(**kwargs)

Bases: Graph2SimplicialLifting

Lift graphs to simplicial complex domain using eccentricity.

Parameters:

**kwargsoptional

Additional arguments for the class.

__init__(**kwargs)

lift_topology(data)

Lift the topology of a graph to a simplicial complex by identifying connected subgraphs as simplices.

Parameters:

datatorch_geometric.data.Data

The input data to be lifted.

Returns:

dict

The lifted topology.

class SimplicialGraphInducedLifting(**kwargs)

Bases: Graph2SimplicialLifting

Lift graphs to simplicial complex domain by identifying connected subgraphs as simplices.

Parameters:

**kwargsoptional

Additional arguments for the class.

__init__(**kwargs)

lift_topology(data)

Lift the topology of a graph to a simplicial complex by identifying connected subgraphs as simplices.

Parameters:

datatorch_geometric.data.Data

The input data to be lifted.

Returns:

dict

The lifted topology.

class SimplicialKHopLifting(max_k_simplices=25, **kwargs)

Bases: Graph2SimplicialLifting

Lift graphs to simplicial complex domain.

The function lifts a graph to a simplicial complex by considering k-hop neighborhoods. For each node its neighborhood is selected and then all the possible simplices, when considering the neighborhood as a clique, are added to the simplicial complex. For this reason this lifting does not conserve the initial graph topology.

Parameters:

max_k_simplicesint, optional

The maximum number of k-simplices to consider. Default is 25.

**kwargsoptional

Additional arguments for the class.

__init__(max_k_simplices=25, **kwargs)

lift_topology(data)

Lift the topology to simplicial complex domain.

Parameters:

datatorch_geometric.data.Data

The input data to be lifted.

Returns:

dict

The lifted topology.

class SimplicialLineLifting(max_simplices=25, **kwargs)

Bases: Graph2SimplicialLifting

Lift graphs to a simplicial complex domain by considering line simplicial complex.

Line simplicial complex is a clique complex of the line graph. Line graph is a graph, in which the vertices are the edges in the initial graph, and two vertices are adjacent if the corresponding edges are adjacent in the initial graph.

Parameters:

max_simplicesint

Max simplices to add for each clique given a rank.

**kwargsoptional

Additional arguments for the class.

__init__(max_simplices=25, **kwargs)

lift_topology(data)

Lift topology of a graph to simplicial domain via line simplicial complex construction.

Parameters:

datatorch_geometric.data.Data

The input data to be lifted.

Returns:

dict

The lifted topology.

class SimplicialVietorisRipsLifting(distance_threshold=1.0, max_simplices=5, **kwargs)

Bases: Graph2SimplicialLifting

Lift graphs to simplicial complex domain using the Vietoris-Rips complex based on pairwise distances.

Parameters:

distance_thresholdfloat

The maximum distance between vertices to form a simplex.

max_simplicesint

Max number of simplices to create for a given node and rank.

**kwargsoptional

Additional arguments for the class.

__init__(distance_threshold=1.0, max_simplices=5, **kwargs)

lift_topology(data)

Lift topology of a graph to a simplicial complex using the Vietoris-Rips complex.

Parameters:

datatorch_geometric.data.Data

The input data to be lifted.

Returns:

dict

The lifted topology.

Submodules

• topobench.transforms.liftings.graph2simplicial.base module
  • Graph2SimplicialLifting
    • Graph2SimplicialLifting.__init__()
  • GraphLifting
    • GraphLifting.__init__()
  • SimplicialComplex
    • SimplicialComplex.__init__()
    • SimplicialComplex.add_elements_from_nx_graph()
    • SimplicialComplex.add_node()
    • SimplicialComplex.add_simplex()
    • SimplicialComplex.add_simplices_from()
    • SimplicialComplex.adjacency_matrix()
    • SimplicialComplex.clone()
    • SimplicialComplex.coadjacency_matrix()
    • SimplicialComplex.coincidence_matrix()
    • SimplicialComplex.dirac_operator_matrix()
    • SimplicialComplex.down_laplacian_matrix()
    • SimplicialComplex.from_gudhi()
    • SimplicialComplex.from_nx()
    • SimplicialComplex.from_spharapy()
    • SimplicialComplex.from_spharpy()
    • SimplicialComplex.from_trimesh()
    • SimplicialComplex.get_all_maximal_simplices()
    • SimplicialComplex.get_boundaries()
    • SimplicialComplex.get_cofaces()
    • SimplicialComplex.get_edges_from_matrix()
    • SimplicialComplex.get_maximal_simplices_of_simplex()
    • SimplicialComplex.get_node_attributes()
    • SimplicialComplex.get_simplex_attributes()
    • SimplicialComplex.get_star()
    • SimplicialComplex.graph_skeleton()
    • SimplicialComplex.hodge_laplacian_matrix()
    • SimplicialComplex.incidence_matrix()
    • SimplicialComplex.is_connected()
    • SimplicialComplex.is_maximal()
    • SimplicialComplex.is_triangular_mesh()
    • SimplicialComplex.laplace_beltrami_operator()
    • SimplicialComplex.load_mesh()
    • SimplicialComplex.normalized_laplacian_matrix()
    • SimplicialComplex.remove_maximal_simplex()
    • SimplicialComplex.remove_nodes()
    • SimplicialComplex.restrict_to_nodes()
    • SimplicialComplex.restrict_to_simplices()
    • SimplicialComplex.set_simplex_attributes()
    • SimplicialComplex.simplicial_closure_of_hypergraph()
    • SimplicialComplex.skeleton()
    • SimplicialComplex.to_cell_complex()
    • SimplicialComplex.to_combinatorial_complex()
    • SimplicialComplex.to_hasse_graph()
    • SimplicialComplex.to_hypergraph()
    • SimplicialComplex.to_spharapy()
    • SimplicialComplex.to_trimesh()
    • SimplicialComplex.up_laplacian_matrix()
    • SimplicialComplex.dim
    • SimplicialComplex.maxdim
    • SimplicialComplex.nodes
    • SimplicialComplex.shape
    • SimplicialComplex.simplices
  • get_complex_connectivity()
• topobench.transforms.liftings.graph2simplicial.clique_lifting module
  • Any
  • Graph2SimplicialLifting
    • Graph2SimplicialLifting.__init__()
  • SimplicialCliqueLifting
    • SimplicialCliqueLifting.__init__()
    • SimplicialCliqueLifting.lift_topology()
  • SimplicialComplex
    • SimplicialComplex.__init__()
    • SimplicialComplex.add_elements_from_nx_graph()
    • SimplicialComplex.add_node()
    • SimplicialComplex.add_simplex()
    • SimplicialComplex.add_simplices_from()
    • SimplicialComplex.adjacency_matrix()
    • SimplicialComplex.clone()
    • SimplicialComplex.coadjacency_matrix()
    • SimplicialComplex.coincidence_matrix()
    • SimplicialComplex.dirac_operator_matrix()
    • SimplicialComplex.down_laplacian_matrix()
    • SimplicialComplex.from_gudhi()
    • SimplicialComplex.from_nx()
    • SimplicialComplex.from_spharapy()
    • SimplicialComplex.from_spharpy()
    • SimplicialComplex.from_trimesh()
    • SimplicialComplex.get_all_maximal_simplices()
    • SimplicialComplex.get_boundaries()
    • SimplicialComplex.get_cofaces()
    • SimplicialComplex.get_edges_from_matrix()
    • SimplicialComplex.get_maximal_simplices_of_simplex()
    • SimplicialComplex.get_node_attributes()
    • SimplicialComplex.get_simplex_attributes()
    • SimplicialComplex.get_star()
    • SimplicialComplex.graph_skeleton()
    • SimplicialComplex.hodge_laplacian_matrix()
    • SimplicialComplex.incidence_matrix()
    • SimplicialComplex.is_connected()
    • SimplicialComplex.is_maximal()
    • SimplicialComplex.is_triangular_mesh()
    • SimplicialComplex.laplace_beltrami_operator()
    • SimplicialComplex.load_mesh()
    • SimplicialComplex.normalized_laplacian_matrix()
    • SimplicialComplex.remove_maximal_simplex()
    • SimplicialComplex.remove_nodes()
    • SimplicialComplex.restrict_to_nodes()
    • SimplicialComplex.restrict_to_simplices()
    • SimplicialComplex.set_simplex_attributes()
    • SimplicialComplex.simplicial_closure_of_hypergraph()
    • SimplicialComplex.skeleton()
    • SimplicialComplex.to_cell_complex()
    • SimplicialComplex.to_combinatorial_complex()
    • SimplicialComplex.to_hasse_graph()
    • SimplicialComplex.to_hypergraph()
    • SimplicialComplex.to_spharapy()
    • SimplicialComplex.to_trimesh()
    • SimplicialComplex.up_laplacian_matrix()
    • SimplicialComplex.dim
    • SimplicialComplex.maxdim
    • SimplicialComplex.nodes
    • SimplicialComplex.shape
    • SimplicialComplex.simplices
  • combinations
• topobench.transforms.liftings.graph2simplicial.dnd_lifting module
  • Data
    • Data.__init__()
    • Data.connected_components()
    • Data.debug()
    • Data.edge_subgraph()
    • Data.from_dict()
    • Data.get_all_edge_attrs()
    • Data.get_all_tensor_attrs()
    • Data.is_edge_attr()
    • Data.is_node_attr()
    • Data.stores_as()
    • Data.subgraph()
    • Data.to_dict()
    • Data.to_heterogeneous()
    • Data.to_namedtuple()
    • Data.update()
    • Data.validate()
    • Data.batch
    • Data.edge_attr
    • Data.edge_index
    • Data.edge_stores
    • Data.edge_weight
    • Data.face
    • Data.node_stores
    • Data.num_edge_features
    • Data.num_edge_types
    • Data.num_faces
    • Data.num_features
    • Data.num_node_features
    • Data.num_node_types
    • Data.num_nodes
    • Data.pos
    • Data.stores
    • Data.time
    • Data.x
    • Data.y
  • Graph2SimplicialLifting
    • Graph2SimplicialLifting.__init__()
  • SimplicialComplex
    • SimplicialComplex.__init__()
    • SimplicialComplex.add_elements_from_nx_graph()
    • SimplicialComplex.add_node()
    • SimplicialComplex.add_simplex()
    • SimplicialComplex.add_simplices_from()
    • SimplicialComplex.adjacency_matrix()
    • SimplicialComplex.clone()
    • SimplicialComplex.coadjacency_matrix()
    • SimplicialComplex.coincidence_matrix()
    • SimplicialComplex.dirac_operator_matrix()
    • SimplicialComplex.down_laplacian_matrix()
    • SimplicialComplex.from_gudhi()
    • SimplicialComplex.from_nx()
    • SimplicialComplex.from_spharapy()
    • SimplicialComplex.from_spharpy()
    • SimplicialComplex.from_trimesh()
    • SimplicialComplex.get_all_maximal_simplices()
    • SimplicialComplex.get_boundaries()
    • SimplicialComplex.get_cofaces()
    • SimplicialComplex.get_edges_from_matrix()
    • SimplicialComplex.get_maximal_simplices_of_simplex()
    • SimplicialComplex.get_node_attributes()
    • SimplicialComplex.get_simplex_attributes()
    • SimplicialComplex.get_star()
    • SimplicialComplex.graph_skeleton()
    • SimplicialComplex.hodge_laplacian_matrix()
    • SimplicialComplex.incidence_matrix()
    • SimplicialComplex.is_connected()
    • SimplicialComplex.is_maximal()
    • SimplicialComplex.is_triangular_mesh()
    • SimplicialComplex.laplace_beltrami_operator()
    • SimplicialComplex.load_mesh()
    • SimplicialComplex.normalized_laplacian_matrix()
    • SimplicialComplex.remove_maximal_simplex()
    • SimplicialComplex.remove_nodes()
    • SimplicialComplex.restrict_to_nodes()
    • SimplicialComplex.restrict_to_simplices()
    • SimplicialComplex.set_simplex_attributes()
    • SimplicialComplex.simplicial_closure_of_hypergraph()
    • SimplicialComplex.skeleton()
    • SimplicialComplex.to_cell_complex()
    • SimplicialComplex.to_combinatorial_complex()
    • SimplicialComplex.to_hasse_graph()
    • SimplicialComplex.to_hypergraph()
    • SimplicialComplex.to_spharapy()
    • SimplicialComplex.to_trimesh()
    • SimplicialComplex.up_laplacian_matrix()
    • SimplicialComplex.dim
    • SimplicialComplex.maxdim
    • SimplicialComplex.nodes
    • SimplicialComplex.shape
    • SimplicialComplex.simplices
  • SimplicialDnDLifting
    • SimplicialDnDLifting.__init__()
    • SimplicialDnDLifting.lift_topology()
  • combinations
• topobench.transforms.liftings.graph2simplicial.eccentricity_lifting module
  • Graph2SimplicialLifting
    • Graph2SimplicialLifting.__init__()
  • SimplicialComplex
    • SimplicialComplex.__init__()
    • SimplicialComplex.add_elements_from_nx_graph()
    • SimplicialComplex.add_node()
    • SimplicialComplex.add_simplex()
    • SimplicialComplex.add_simplices_from()
    • SimplicialComplex.adjacency_matrix()
    • SimplicialComplex.clone()
    • SimplicialComplex.coadjacency_matrix()
    • SimplicialComplex.coincidence_matrix()
    • SimplicialComplex.dirac_operator_matrix()
    • SimplicialComplex.down_laplacian_matrix()
    • SimplicialComplex.from_gudhi()
    • SimplicialComplex.from_nx()
    • SimplicialComplex.from_spharapy()
    • SimplicialComplex.from_spharpy()
    • SimplicialComplex.from_trimesh()
    • SimplicialComplex.get_all_maximal_simplices()
    • SimplicialComplex.get_boundaries()
    • SimplicialComplex.get_cofaces()
    • SimplicialComplex.get_edges_from_matrix()
    • SimplicialComplex.get_maximal_simplices_of_simplex()
    • SimplicialComplex.get_node_attributes()
    • SimplicialComplex.get_simplex_attributes()
    • SimplicialComplex.get_star()
    • SimplicialComplex.graph_skeleton()
    • SimplicialComplex.hodge_laplacian_matrix()
    • SimplicialComplex.incidence_matrix()
    • SimplicialComplex.is_connected()
    • SimplicialComplex.is_maximal()
    • SimplicialComplex.is_triangular_mesh()
    • SimplicialComplex.laplace_beltrami_operator()
    • SimplicialComplex.load_mesh()
    • SimplicialComplex.normalized_laplacian_matrix()
    • SimplicialComplex.remove_maximal_simplex()
    • SimplicialComplex.remove_nodes()
    • SimplicialComplex.restrict_to_nodes()
    • SimplicialComplex.restrict_to_simplices()
    • SimplicialComplex.set_simplex_attributes()
    • SimplicialComplex.simplicial_closure_of_hypergraph()
    • SimplicialComplex.skeleton()
    • SimplicialComplex.to_cell_complex()
    • SimplicialComplex.to_combinatorial_complex()
    • SimplicialComplex.to_hasse_graph()
    • SimplicialComplex.to_hypergraph()
    • SimplicialComplex.to_spharapy()
    • SimplicialComplex.to_trimesh()
    • SimplicialComplex.up_laplacian_matrix()
    • SimplicialComplex.dim
    • SimplicialComplex.maxdim
    • SimplicialComplex.nodes
    • SimplicialComplex.shape
    • SimplicialComplex.simplices
  • SimplicialEccentricityLifting
    • SimplicialEccentricityLifting.__init__()
    • SimplicialEccentricityLifting.lift_topology()
  • combinations
• topobench.transforms.liftings.graph2simplicial.graph_induced_lifting module
  • Graph2SimplicialLifting
    • Graph2SimplicialLifting.__init__()
  • SimplicialComplex
    • SimplicialComplex.__init__()
    • SimplicialComplex.add_elements_from_nx_graph()
    • SimplicialComplex.add_node()
    • SimplicialComplex.add_simplex()
    • SimplicialComplex.add_simplices_from()
    • SimplicialComplex.adjacency_matrix()
    • SimplicialComplex.clone()
    • SimplicialComplex.coadjacency_matrix()
    • SimplicialComplex.coincidence_matrix()
    • SimplicialComplex.dirac_operator_matrix()
    • SimplicialComplex.down_laplacian_matrix()
    • SimplicialComplex.from_gudhi()
    • SimplicialComplex.from_nx()
    • SimplicialComplex.from_spharapy()
    • SimplicialComplex.from_spharpy()
    • SimplicialComplex.from_trimesh()
    • SimplicialComplex.get_all_maximal_simplices()
    • SimplicialComplex.get_boundaries()
    • SimplicialComplex.get_cofaces()
    • SimplicialComplex.get_edges_from_matrix()
    • SimplicialComplex.get_maximal_simplices_of_simplex()
    • SimplicialComplex.get_node_attributes()
    • SimplicialComplex.get_simplex_attributes()
    • SimplicialComplex.get_star()
    • SimplicialComplex.graph_skeleton()
    • SimplicialComplex.hodge_laplacian_matrix()
    • SimplicialComplex.incidence_matrix()
    • SimplicialComplex.is_connected()
    • SimplicialComplex.is_maximal()
    • SimplicialComplex.is_triangular_mesh()
    • SimplicialComplex.laplace_beltrami_operator()
    • SimplicialComplex.load_mesh()
    • SimplicialComplex.normalized_laplacian_matrix()
    • SimplicialComplex.remove_maximal_simplex()
    • SimplicialComplex.remove_nodes()
    • SimplicialComplex.restrict_to_nodes()
    • SimplicialComplex.restrict_to_simplices()
    • SimplicialComplex.set_simplex_attributes()
    • SimplicialComplex.simplicial_closure_of_hypergraph()
    • SimplicialComplex.skeleton()
    • SimplicialComplex.to_cell_complex()
    • SimplicialComplex.to_combinatorial_complex()
    • SimplicialComplex.to_hasse_graph()
    • SimplicialComplex.to_hypergraph()
    • SimplicialComplex.to_spharapy()
    • SimplicialComplex.to_trimesh()
    • SimplicialComplex.up_laplacian_matrix()
    • SimplicialComplex.dim
    • SimplicialComplex.maxdim
    • SimplicialComplex.nodes
    • SimplicialComplex.shape
    • SimplicialComplex.simplices
  • SimplicialGraphInducedLifting
    • SimplicialGraphInducedLifting.__init__()
    • SimplicialGraphInducedLifting.lift_topology()
  • combinations
• topobench.transforms.liftings.graph2simplicial.khop_lifting module
  • Any
  • Graph2SimplicialLifting
    • Graph2SimplicialLifting.__init__()
  • SimplicialComplex
    • SimplicialComplex.__init__()
    • SimplicialComplex.add_elements_from_nx_graph()
    • SimplicialComplex.add_node()
    • SimplicialComplex.add_simplex()
    • SimplicialComplex.add_simplices_from()
    • SimplicialComplex.adjacency_matrix()
    • SimplicialComplex.clone()
    • SimplicialComplex.coadjacency_matrix()
    • SimplicialComplex.coincidence_matrix()
    • SimplicialComplex.dirac_operator_matrix()
    • SimplicialComplex.down_laplacian_matrix()
    • SimplicialComplex.from_gudhi()
    • SimplicialComplex.from_nx()
    • SimplicialComplex.from_spharapy()
    • SimplicialComplex.from_spharpy()
    • SimplicialComplex.from_trimesh()
    • SimplicialComplex.get_all_maximal_simplices()
    • SimplicialComplex.get_boundaries()
    • SimplicialComplex.get_cofaces()
    • SimplicialComplex.get_edges_from_matrix()
    • SimplicialComplex.get_maximal_simplices_of_simplex()
    • SimplicialComplex.get_node_attributes()
    • SimplicialComplex.get_simplex_attributes()
    • SimplicialComplex.get_star()
    • SimplicialComplex.graph_skeleton()
    • SimplicialComplex.hodge_laplacian_matrix()
    • SimplicialComplex.incidence_matrix()
    • SimplicialComplex.is_connected()
    • SimplicialComplex.is_maximal()
    • SimplicialComplex.is_triangular_mesh()
    • SimplicialComplex.laplace_beltrami_operator()
    • SimplicialComplex.load_mesh()
    • SimplicialComplex.normalized_laplacian_matrix()
    • SimplicialComplex.remove_maximal_simplex()
    • SimplicialComplex.remove_nodes()
    • SimplicialComplex.restrict_to_nodes()
    • SimplicialComplex.restrict_to_simplices()
    • SimplicialComplex.set_simplex_attributes()
    • SimplicialComplex.simplicial_closure_of_hypergraph()
    • SimplicialComplex.skeleton()
    • SimplicialComplex.to_cell_complex()
    • SimplicialComplex.to_combinatorial_complex()
    • SimplicialComplex.to_hasse_graph()
    • SimplicialComplex.to_hypergraph()
    • SimplicialComplex.to_spharapy()
    • SimplicialComplex.to_trimesh()
    • SimplicialComplex.up_laplacian_matrix()
    • SimplicialComplex.dim
    • SimplicialComplex.maxdim
    • SimplicialComplex.nodes
    • SimplicialComplex.shape
    • SimplicialComplex.simplices
  • SimplicialKHopLifting
    • SimplicialKHopLifting.__init__()
    • SimplicialKHopLifting.lift_topology()
  • combinations
  • tqdm
    • tqdm.__init__()
    • tqdm.clear()
    • tqdm.close()
    • tqdm.display()
    • tqdm.external_write_mode()
    • tqdm.format_interval()
    • tqdm.format_meter()
    • tqdm.format_num()
    • tqdm.format_sizeof()
    • tqdm.get_lock()
    • tqdm.moveto()
    • tqdm.pandas()
    • tqdm.refresh()
    • tqdm.reset()
    • tqdm.set_description()
    • tqdm.set_description_str()
    • tqdm.set_lock()
    • tqdm.set_postfix()
    • tqdm.set_postfix_str()
    • tqdm.status_printer()
    • tqdm.unpause()
    • tqdm.update()
    • tqdm.wrapattr()
    • tqdm.write()
    • tqdm.format_dict
    • tqdm.monitor
    • tqdm.monitor_interval
• topobench.transforms.liftings.graph2simplicial.latentclique_lifting module
  • Graph2SimplicialLifting
    • Graph2SimplicialLifting.__init__()
  • LatentCliqueLifting
    • LatentCliqueLifting.__init__()
    • LatentCliqueLifting.lift_topology()
  • SimplicialCliqueLifting
    • SimplicialCliqueLifting.__init__()
    • SimplicialCliqueLifting.lift_topology()
  • tqdm
  • logsumexp()
• topobench.transforms.liftings.graph2simplicial.line_lifting module
  • Any
  • Graph2SimplicialLifting
    • Graph2SimplicialLifting.__init__()
  • SimplicialComplex
    • SimplicialComplex.__init__()
    • SimplicialComplex.add_elements_from_nx_graph()
    • SimplicialComplex.add_node()
    • SimplicialComplex.add_simplex()
    • SimplicialComplex.add_simplices_from()
    • SimplicialComplex.adjacency_matrix()
    • SimplicialComplex.clone()
    • SimplicialComplex.coadjacency_matrix()
    • SimplicialComplex.coincidence_matrix()
    • SimplicialComplex.dirac_operator_matrix()
    • SimplicialComplex.down_laplacian_matrix()
    • SimplicialComplex.from_gudhi()
    • SimplicialComplex.from_nx()
    • SimplicialComplex.from_spharapy()
    • SimplicialComplex.from_spharpy()
    • SimplicialComplex.from_trimesh()
    • SimplicialComplex.get_all_maximal_simplices()
    • SimplicialComplex.get_boundaries()
    • SimplicialComplex.get_cofaces()
    • SimplicialComplex.get_edges_from_matrix()
    • SimplicialComplex.get_maximal_simplices_of_simplex()
    • SimplicialComplex.get_node_attributes()
    • SimplicialComplex.get_simplex_attributes()
    • SimplicialComplex.get_star()
    • SimplicialComplex.graph_skeleton()
    • SimplicialComplex.hodge_laplacian_matrix()
    • SimplicialComplex.incidence_matrix()
    • SimplicialComplex.is_connected()
    • SimplicialComplex.is_maximal()
    • SimplicialComplex.is_triangular_mesh()
    • SimplicialComplex.laplace_beltrami_operator()
    • SimplicialComplex.load_mesh()
    • SimplicialComplex.normalized_laplacian_matrix()
    • SimplicialComplex.remove_maximal_simplex()
    • SimplicialComplex.remove_nodes()
    • SimplicialComplex.restrict_to_nodes()
    • SimplicialComplex.restrict_to_simplices()
    • SimplicialComplex.set_simplex_attributes()
    • SimplicialComplex.simplicial_closure_of_hypergraph()
    • SimplicialComplex.skeleton()
    • SimplicialComplex.to_cell_complex()
    • SimplicialComplex.to_combinatorial_complex()
    • SimplicialComplex.to_hasse_graph()
    • SimplicialComplex.to_hypergraph()
    • SimplicialComplex.to_spharapy()
    • SimplicialComplex.to_trimesh()
    • SimplicialComplex.up_laplacian_matrix()
    • SimplicialComplex.dim
    • SimplicialComplex.maxdim
    • SimplicialComplex.nodes
    • SimplicialComplex.shape
    • SimplicialComplex.simplices
  • SimplicialLineLifting
    • SimplicialLineLifting.__init__()
    • SimplicialLineLifting.lift_topology()
  • combinations
• topobench.transforms.liftings.graph2simplicial.neighborhood_complex_lifting module
  • Any
  • Data
    • Data.__init__()
    • Data.connected_components()
    • Data.debug()
    • Data.edge_subgraph()
    • Data.from_dict()
    • Data.get_all_edge_attrs()
    • Data.get_all_tensor_attrs()
    • Data.is_edge_attr()
    • Data.is_node_attr()
    • Data.stores_as()
    • Data.subgraph()
    • Data.to_dict()
    • Data.to_heterogeneous()
    • Data.to_namedtuple()
    • Data.update()
    • Data.validate()
    • Data.batch
    • Data.edge_attr
    • Data.edge_index
    • Data.edge_stores
    • Data.edge_weight
    • Data.face
    • Data.node_stores
    • Data.num_edge_features
    • Data.num_edge_types
    • Data.num_faces
    • Data.num_features
    • Data.num_node_features
    • Data.num_node_types
    • Data.num_nodes
    • Data.pos
    • Data.stores
    • Data.time
    • Data.x
    • Data.y
  • Graph2SimplicialLifting
    • Graph2SimplicialLifting.__init__()
  • NeighborhoodComplexLifting
    • NeighborhoodComplexLifting.__init__()
    • NeighborhoodComplexLifting.lift_topology()
  • SimplicialComplex
    • SimplicialComplex.__init__()
    • SimplicialComplex.add_elements_from_nx_graph()
    • SimplicialComplex.add_node()
    • SimplicialComplex.add_simplex()
    • SimplicialComplex.add_simplices_from()
    • SimplicialComplex.adjacency_matrix()
    • SimplicialComplex.clone()
    • SimplicialComplex.coadjacency_matrix()
    • SimplicialComplex.coincidence_matrix()
    • SimplicialComplex.dirac_operator_matrix()
    • SimplicialComplex.down_laplacian_matrix()
    • SimplicialComplex.from_gudhi()
    • SimplicialComplex.from_nx()
    • SimplicialComplex.from_spharapy()
    • SimplicialComplex.from_spharpy()
    • SimplicialComplex.from_trimesh()
    • SimplicialComplex.get_all_maximal_simplices()
    • SimplicialComplex.get_boundaries()
    • SimplicialComplex.get_cofaces()
    • SimplicialComplex.get_edges_from_matrix()
    • SimplicialComplex.get_maximal_simplices_of_simplex()
    • SimplicialComplex.get_node_attributes()
    • SimplicialComplex.get_simplex_attributes()
    • SimplicialComplex.get_star()
    • SimplicialComplex.graph_skeleton()
    • SimplicialComplex.hodge_laplacian_matrix()
    • SimplicialComplex.incidence_matrix()
    • SimplicialComplex.is_connected()
    • SimplicialComplex.is_maximal()
    • SimplicialComplex.is_triangular_mesh()
    • SimplicialComplex.laplace_beltrami_operator()
    • SimplicialComplex.load_mesh()
    • SimplicialComplex.normalized_laplacian_matrix()
    • SimplicialComplex.remove_maximal_simplex()
    • SimplicialComplex.remove_nodes()
    • SimplicialComplex.restrict_to_nodes()
    • SimplicialComplex.restrict_to_simplices()
    • SimplicialComplex.set_simplex_attributes()
    • SimplicialComplex.simplicial_closure_of_hypergraph()
    • SimplicialComplex.skeleton()
    • SimplicialComplex.to_cell_complex()
    • SimplicialComplex.to_combinatorial_complex()
    • SimplicialComplex.to_hasse_graph()
    • SimplicialComplex.to_hypergraph()
    • SimplicialComplex.to_spharapy()
    • SimplicialComplex.to_trimesh()
    • SimplicialComplex.up_laplacian_matrix()
    • SimplicialComplex.dim
    • SimplicialComplex.maxdim
    • SimplicialComplex.nodes
    • SimplicialComplex.shape
    • SimplicialComplex.simplices
  • combinations
  • tqdm
    • tqdm.__init__()
    • tqdm.clear()
    • tqdm.close()
    • tqdm.display()
    • tqdm.external_write_mode()
    • tqdm.format_interval()
    • tqdm.format_meter()
    • tqdm.format_num()
    • tqdm.format_sizeof()
    • tqdm.get_lock()
    • tqdm.moveto()
    • tqdm.pandas()
    • tqdm.refresh()
    • tqdm.reset()
    • tqdm.set_description()
    • tqdm.set_description_str()
    • tqdm.set_lock()
    • tqdm.set_postfix()
    • tqdm.set_postfix_str()
    • tqdm.status_printer()
    • tqdm.unpause()
    • tqdm.update()
    • tqdm.wrapattr()
    • tqdm.write()
    • tqdm.format_dict
    • tqdm.monitor
    • tqdm.monitor_interval
  • to_undirected()
• topobench.transforms.liftings.graph2simplicial.vietoris_rips_lifting module
  • Graph2SimplicialLifting
    • Graph2SimplicialLifting.__init__()
  • SimplicialComplex
    • SimplicialComplex.__init__()
    • SimplicialComplex.add_elements_from_nx_graph()
    • SimplicialComplex.add_node()
    • SimplicialComplex.add_simplex()
    • SimplicialComplex.add_simplices_from()
    • SimplicialComplex.adjacency_matrix()
    • SimplicialComplex.clone()
    • SimplicialComplex.coadjacency_matrix()
    • SimplicialComplex.coincidence_matrix()
    • SimplicialComplex.dirac_operator_matrix()
    • SimplicialComplex.down_laplacian_matrix()
    • SimplicialComplex.from_gudhi()
    • SimplicialComplex.from_nx()
    • SimplicialComplex.from_spharapy()
    • SimplicialComplex.from_spharpy()
    • SimplicialComplex.from_trimesh()
    • SimplicialComplex.get_all_maximal_simplices()
    • SimplicialComplex.get_boundaries()
    • SimplicialComplex.get_cofaces()
    • SimplicialComplex.get_edges_from_matrix()
    • SimplicialComplex.get_maximal_simplices_of_simplex()
    • SimplicialComplex.get_node_attributes()
    • SimplicialComplex.get_simplex_attributes()
    • SimplicialComplex.get_star()
    • SimplicialComplex.graph_skeleton()
    • SimplicialComplex.hodge_laplacian_matrix()
    • SimplicialComplex.incidence_matrix()
    • SimplicialComplex.is_connected()
    • SimplicialComplex.is_maximal()
    • SimplicialComplex.is_triangular_mesh()
    • SimplicialComplex.laplace_beltrami_operator()
    • SimplicialComplex.load_mesh()
    • SimplicialComplex.normalized_laplacian_matrix()
    • SimplicialComplex.remove_maximal_simplex()
    • SimplicialComplex.remove_nodes()
    • SimplicialComplex.restrict_to_nodes()
    • SimplicialComplex.restrict_to_simplices()
    • SimplicialComplex.set_simplex_attributes()
    • SimplicialComplex.simplicial_closure_of_hypergraph()
    • SimplicialComplex.skeleton()
    • SimplicialComplex.to_cell_complex()
    • SimplicialComplex.to_combinatorial_complex()
    • SimplicialComplex.to_hasse_graph()
    • SimplicialComplex.to_hypergraph()
    • SimplicialComplex.to_spharapy()
    • SimplicialComplex.to_trimesh()
    • SimplicialComplex.up_laplacian_matrix()
    • SimplicialComplex.dim
    • SimplicialComplex.maxdim
    • SimplicialComplex.nodes
    • SimplicialComplex.shape
    • SimplicialComplex.simplices
  • SimplicialVietorisRipsLifting
    • SimplicialVietorisRipsLifting.__init__()
    • SimplicialVietorisRipsLifting.lift_topology()
  • tqdm
    • tqdm.__init__()
    • tqdm.clear()
    • tqdm.close()
    • tqdm.display()
    • tqdm.external_write_mode()
    • tqdm.format_interval()
    • tqdm.format_meter()
    • tqdm.format_num()
    • tqdm.format_sizeof()
    • tqdm.get_lock()
    • tqdm.moveto()
    • tqdm.pandas()
    • tqdm.refresh()
    • tqdm.reset()
    • tqdm.set_description()
    • tqdm.set_description_str()
    • tqdm.set_lock()
    • tqdm.set_postfix()
    • tqdm.set_postfix_str()
    • tqdm.status_printer()
    • tqdm.unpause()
    • tqdm.update()
    • tqdm.wrapattr()
    • tqdm.write()
    • tqdm.format_dict
    • tqdm.monitor
    • tqdm.monitor_interval
  • nodes_search()