ts2vg.HorizontalVG

class ts2vg.HorizontalVG(*, directed=None, weighted=None, min_weight=None, max_weight=None, penetrable_limit=0)

Horizontal Visibility Graph.

Used to transform a time series to a Horizontal Visibility Graph.

Parameters

• directed (str, None) – If None make an undirected graph, otherwise, a directed graph by using one of the following values: 'left_to_right', 'top_to_bottom'. See Directed graphs for more information. Default None.

• weighted (str, None) – If None make an unweighted graph, otherwise, a weighted graph by using one of the following values: 'distance', 'sq_distance', 'v_distance', 'abs_v_distance', 'h_distance', 'abs_h_distance', 'slope', 'abs_slope', 'angle', 'abs_angle', 'num_penetrations'. See Weighted graphs for more information. Default None.

• min_weight (float, None) – If provided, only edges with a weight higher than min_weight (non inclusive) will be included in the final graph. The graph must be weighted and the values used for weight will depend on the weighted parameter. This acts as a generalization of parametric visibility graphs. Default None.

• max_weight (float, None) – If provided, only edges with a weight lower than max_weight (non inclusive) will be included in the final graph. The graph must be weighted and the values used for weight will depend on the weighted parameter. This acts as a generalization of parametric visibility graphs. Default None.

• penetrable_limit (int) – If larger than 0, make a limited penetrable horizontal visibility graph (LPHVG). The value for penetrable_limit indicates the maximum number of data points that are allowed to obstruct the visibility between two nodes that can still be connected in the final graph. Default 0 (regular non-penetrable visibility graph).

References

• Lucas Lacasa et al., “Horizontal visibility graphs: exact results for random time series”, 2009.

• Xin Lan et al., “Fast transformation from time series to visibility graphs”, 2015.

Examples

from ts2vg import HorizontalVG

ts = [1.0, 0.5, 0.3, 0.7, 1.0, 0.5, 0.3, 0.8]

g = HorizontalVG()
g.build(ts)

edges = g.edges

Attributes

degree_counts	Degree counts of the graph.
degree_distribution	Degree distribution of the graph.
degrees	Degree sequence of the graph.
degrees_in
degrees_out
edges	List of edges (links) of the graph.
edges_unweighted	List of edges of the graph without including the weights.
is_directed	True if the graph is directed, False otherwise.
is_weighted	True if the graph is weighted, False otherwise.
n_edges	Number of edges (links) in the graph.
n_vertices	Number of vertices (nodes) in the graph.
weights	Weights of the edges of the graph.

Methods

adjacency_matrix([triangle, use_weights, …])	Adjacency matrix of the graph.
as_igraph()	Return an igraph graph object corresponding to this graph.
as_networkx()	Return a NetworkX graph object corresponding to this graph.
as_snap()	Return a SNAP graph object corresponding to this graph.
build(ts[, xs, only_degrees])	Compute and build the visibility graph for the given time series.
node_positions()	Dictionary with nodes as keys and positions (x, y) as values.
summary([prints, title])	Prints (or returns) a simple text summary describing the visibility graph.

Attribute details

degree_counts

Degree counts of the graph.

Two lists ks, cs are returned. cs[i] is the number of nodes in the graph that have degree ks[i].

The count of any other degree value not listed in ks is 0.

degree_distribution

Degree distribution of the graph.

Two lists ks, ps are returned. ps[i] is the empirical probability that a node in the graph has degree ks[i].

The probability for any other degree value not listed in ks is 0.

degrees

Degree sequence of the graph.

Return a list of degree values for each node in the graph, in the same order as the input time series.

degrees_in

degrees_out

edges

List of edges (links) of the graph.

If the graph is unweighted, a list of tuple pairs (source_node, target_node). If the graph is weighted, an iterable of tuple triplets (source_node, target_node, weight).

Nodes are identified using an integer from 0 to n-1 assigned sequentially in the same order as the input time series.

edges_unweighted

List of edges of the graph without including the weights.

A list of tuple pairs (source_node, target_node). For unweighted graphs this is the same as edges.

Nodes are identified using an integer from 0 to n-1 assigned sequentially in the same order as the input time series.

is_directed

True if the graph is directed, False otherwise.

is_weighted

True if the graph is weighted, False otherwise.

n_edges

Number of edges (links) in the graph.

n_vertices

Number of vertices (nodes) in the graph.

weights

Weights of the edges of the graph.

Return a 1D array containing the weights of the edges of the graph (listed in the same order as in edges). None if the graph is unweighted.

Method details

adjacency_matrix(triangle='both', use_weights=False, no_weight_value=nan)

Adjacency matrix of the graph.

Parameters

• triangle (str) –

  One of 'lower' (uses the lower triangle of the matrix), 'upper' (uses the upper triangle of the matrix) or 'both' (uses both). Only applicable for undirected graphs.

  Default 'both'.

• use_weights (bool) –

  If True, return an adjacency matrix containing the edge weights, otherwise return a binary adjacency matrix. Only applicable for weighted graphs.

  Default False.

• no_weight_value (float) –

  The default value used in the matrix for the cases where the nodes are not connected. Only applicable for weighted graphs and when using use_weights=True.

  Default np.nan.

Returns

2D array – Adjacency matrix of the graph.

as_igraph()

Return an igraph graph object corresponding to this graph.

The igraph package is required.

as_networkx()

Return a NetworkX graph object corresponding to this graph.

The networkx package is required.

as_snap()

Return a SNAP graph object corresponding to this graph.

The snap package is required.

build(ts, xs=None, only_degrees=False)

Compute and build the visibility graph for the given time series.

Parameters

• ts (1D array like) – Input time series.

• xs (1D array like, optional) –

  X coordinates for the time series. Length of xs must match length of ts.

  If not provided, [0, 1, 2...] will be used.

• only_degrees (bool) – If True only compute the graph degrees, otherwise compute the whole graph. Default False.

Returns

self

node_positions()

Dictionary with nodes as keys and positions (x, y) as values.

summary(prints=True, title='Visibility Graph')

Prints (or returns) a simple text summary describing the visibility graph.

Parameters

• prints (bool) – If True prints the summary, otherwise returns the summary as a string. Default True.

• title (str) – Title for the table. Default is ‘Visibility Graph’.

Returns

str – A string containing the short summary (only if prints=False).