The quantum graph module

Quantum graph construction module.

A quantum graph is a networkx graph with additional parameters in graph.graph[‘param’] and specific node/edges attributes.

netsalt.quantum_graph.construct_incidence_matrix(graph)

Construct the quantum incidence matrix B(k).

Parameters

graph (graph) – quantum graph

netsalt.quantum_graph.construct_laplacian(wavenumber, graph)

Construct quantum laplacian from a graph.

The quantum laplacian is L(k) = B^T(k) W^{-1}(k) B(k), with quantum incidence and weight matrix.

Parameters

• wavenumber (complex) – wavenumber

• graph (graph) – quantum graph

netsalt.quantum_graph.construct_weight_matrix(graph, with_k=True)

Construct the quantum matrix W^{-1}(k).

The with_k argument is needed for the graph laplcian, not for computing the edge amplitudes.

Parameters

• graph (graph) – quantum graph

• with_k (bool) – multiplies or not the laplacian by k

netsalt.quantum_graph.create_quantum_graph(graph, params=None, positions=None, lengths=None, seed=42, noise_level=0.001)

Extend a networkx graph with necessary attributes for being a quantum graph.

Parameters

• graph (networkx graph) – pure networkx graph to consider as a quantum graph

• params (dict) – specific parameters to setup the quantum graph (depends on use cases)

• positions (list) – node positions, if Non networkx.spring_layout is used

• lengths (list) –

• seed (int) – seed for rng

• noise_level (float) – adds some noise if too manuy edges of equal lengths are found

netsalt.quantum_graph.get_total_inner_length(graph)

Get the total inner length of the graph (considering inner edges only).

Inner edges are defined as edges without degree one nodes.

Parameters

graph (graph) – quantum graph

netsalt.quantum_graph.get_total_length(graph)

Get the total length of a quantum graph.

Parameters

graph (graph) – quantum graph

netsalt.quantum_graph.laplacian_quality(laplacian, method='eigenvalue')

Return the quality of a mode encoded in the quantum laplacian.

If quality is low, the wavenumber of the laplacian is close to a solution of the quantum graph.

Parameters

• laplacian (sparse matrix) – laplacian matrix

• method (str) – either eigenvalue or singular value

netsalt.quantum_graph.mode_quality(mode, graph)

Quality of a mode, small means good quality, thus the mode is close to a correct mode.

Parameters

• mode (complex) – complex mode

• graph (graph) – quantum graph

netsalt.quantum_graph.oversample_graph(graph, edge_size)

Oversample a graph by adding points on edges.

Parameters

• graph (graph) – quantum graph

• edge_size (float) – edge size to sample the graph

netsalt.quantum_graph.set_inner_edges(graph, params=None, outer_edges=None)

Set the inner edges to True, according to a given model in params[‘open_model’].

WARNING: this modifies params, which has to be set to graph with update_parameters TODO: improve implementation along with update_parameters

Parameters

• graph (graph) – quantum graph

• params (dict) – has to contain ‘open_model’ of the form open, closed, custom

• outer_edges (list) – if open_model == custom, pass the list of outer edges.

netsalt.quantum_graph.set_total_length(graph, total_length=None, max_extent=None, inner=True, with_position=True)

Set the (inner) total lengths of the graph to a given value.

Parameters

• graph (graph) – quantum graph

• total_length (float) – total length to set

• max_extent (float) – only if total_length is None, set the maximal extent

• inner (bool) – if True, only consider inner edges

• with_position (bool) – if True, also rescale node positions

netsalt.quantum_graph.set_wavenumber(graph, wavenumber)

Set edge wavenumbers with dispersion relation defined in graph[‘dispersion_relation’].

Parameters

• wavenumber (complex) – wavenumber

• graph (graph) – quantum graph

netsalt.quantum_graph.simplify_graph(graph)

Remove degree 2 nodes.

Parameters

graph (graph) – quantum graph

netsalt.quantum_graph.update_parameters(graph, params, force=False)

Set the parameter dictionary to the graph.

TODO: improve this implementation

Parameters

• graph (graph) – quantum graph

• params (dict) – specific parameters to setup the quantum graph (depends on use cases)

• force (bool) – I forgot