permaviss.simplicial_complexes.flag_complex

Functions

flag_complex(G, no_vertices, max_dim)

Compute the flag complex of a graph G up to a maximum dimension max_dim.

permaviss.simplicial_complexes.flag_complex._lower_neighbours(G, u)

Given a graph G and a vertex u in G, we return a list with the vertices in G that are lower than u and are connected to u by an edge in G.

Parameters:

• G (Numpy Array(no. of edges, 2)) – Matrix storing the edges of the graph.
• u (int) – Vertex of the graph.

Returns:

lower_neighbours – List of lower neighbours of u in G.

Return type:

list

permaviss.simplicial_complexes.flag_complex.flag_complex(G, no_vertices, max_dim)

Compute the flag complex of a graph G up to a maximum dimension max_dim.

Parameters:

• G (Numpy Array(no. of edges, 2)) – Matrix storing the edges of the graph.
• no_vertices (int) – Number of vertices in graph G
• max_dim (int) – Maximum dimension

Returns:

fl_cpx – Flag complex of G. The 0 entry stores the number of vertices. For a higher entry i, fl_cpx[i] stores a Numpy Array matrix with the i simplices from fl_cpx.

Return type:

list(Numpy Array)