Simplicial complex module

Representation of simplicial complex

simplicial_kuramoto.simplicial_complex.pos(matrix)

Return positive part of matrix.

simplicial_kuramoto.simplicial_complex.neg(matrix)

Return negative part of matrix.

class simplicial_kuramoto.simplicial_complex.SimplicialComplex(graph=None, faces=None, no_faces=False, face_weights=None)

Class representing a simplicial complex.

Initialise the class.

Parameters:

• graph (networkx) – original graph to consider

• faces (list) – list of faces, each element is a list of ordered 3 nodes

set_faces(faces=None)

Set faces from list of triangles if provided, or all triangles.

set_lexicographic()

Set orientation of edges in lexicographic order.

flip_edge_orientation(edge_indices)

Flip the orientation of an edge.

property W0

Create node weight matrix.

property W1

Create edge weight matrix.

property W2

Create face weight matrix.

property B0

Create node incidence matrix.

property N0

Create weighted node incidence matrix.

property N0s

Create conjugate weighted node incidence matrix.

property B1

Create edge incidence matrix.

property N1s

Create conjugate weighted node incidence matrix.

property N1

Create conjugate weighted edge incidence matrix.

property L0

Compute the node laplacian.

property L1

Compute the edge laplacian.

property V0

Lift operator on nodes.

property V1

Lift operator on edges.

property V2

Lift operator on faces.

property lifted_N0

Create lifted version of incidence matrices.

property lifted_N0s

Create lifted version of incidence matrices.

property lifted_N0s_left

Create lifted version of incidence matrices.

property lifted_N0n

Create lifted version of incidence matrices.

property lifted_N0n_right

Create lifted version of incidence matrices.

property lifted_N0sn

Create lifted version of incidence matrices.

property lifted_N1

Create lifted version of incidence matrices.

property lifted_N1n_right

Create lifted version of incidence matrices.

property lifted_N1s_left

Create lifted version of incidence matrices.

property lifted_N1sn

Create lifted version of incidence matrices.

simplicial_kuramoto.simplicial_complex.use_with_xgi(func)

Use this as a decorator to convert xgi simplicial complex to internal structure.

First argument of the functiou should be a SimplicialComplex object (internal of xgi)

simplicial_kuramoto.simplicial_complex.xgi_to_internal(simplicial_complex)

Convert xgi simplicial complex into internal simplicial complex structure.