Transform#
Methods to lift a graph to a cell complex.
- toponetx.transform.graph_to_cell_complex.homology_cycle_cell_complex(G) CellComplex[source]#
Get the cell complex obtained by adding homology cycles of a graph.
- Parameters:
- Gnetworkx graph
Input graph.
- Returns:
- CellComplex
The cell complex obtained by adding the homology cycles of the graph.
Methods to lift a graph to a simplicial complex.
- toponetx.transform.graph_to_simplicial_complex.graph_to_clique_complex(G: Graph, max_rank: int | None = None) SimplicialComplex[source]#
Get the clique complex of a graph.
- Parameters:
- Gnetworks.Graph
Input graph.
- max_rankint, optional
The maximum rank of the simplices in the output clique complex.
- Returns:
- SimplicialComplex
The clique simplicial complex of rank max_rank of the graph G.
- toponetx.transform.graph_to_simplicial_complex.graph_to_neighbor_complex(G: Graph) SimplicialComplex[source]#
Get the neighbor complex of a graph.
- Parameters:
- Gnetworkx.Graph
Input graph.
- Returns:
- toponetx.classes.SimplicialComplex
The neighbor complex of the graph.
Notes
This type of simplicial complexes can have very large dimension (max degree of the graph) and it is a function of the distribution of the valency of the graph.
- toponetx.transform.graph_to_simplicial_complex.weighted_graph_to_vietoris_rips_complex(G: Graph, r: float, max_dim: int | None = None)[source]#
Get the Vietoris-Rips complex of radius r of a weighted undirected graph.
The Vietoris-Rips complex of radius r is the clique complex given by the cliques of G whose nodes have pairwise distances less or equal than r. All vertices are added to the Vietoris-Rips complex regardless of the radius introduced.
If G is a clique weighted by a dissimilarity function d that satisfies max_v d(v, v) <= min d(u,v) for u != v, and r >= d(v, v) for all nodes v, then the Vietoris-Rips complex of radius r is the usual Vietoris-Rips abstract simplicial complex of radius r for point clouds with dissimilarities.
- Parameters:
- Gnetworkx.Graph
Weighted undirected input graph. The weights of the edges must be in the attribute ‘weight’.
- rfloat
The radius for the Vietoris-Rips simplicial complex computation.
- max_dimint, optional
The max dimension of the cliques in the output clique complex.
- Returns:
- SimplicialComplex
The Vietoris-Rips simplicial complex of dimension max_dim of the graph G.