libpysal.weights.Gabriel¶

class libpysal.weights.Gabriel(coordinates, **kwargs)[source]¶

Constructs the Gabriel graph of a set of points. This graph is a subset of the Delaunay triangulation where only “short” links are retained. This function is also accelerated using numba, and implemented on top of the scipy.spatial.Delaunay class.

For a link (i,j) connecting node i to j in the Delaunay triangulation to be retained in the Gabriel graph, it must pass a point set exclusion test:

Construct the circle C_ij containing link (i,j) as its diameter
If any other node k is contained within C_ij, then remove link (i,j) from the graph.
Once all links are evaluated, the remaining graph is the Gabriel graph.

Parameters:

coordinatesarray of points, (N,2): numpy array of coordinates containing locations to compute the delaunay triangulation
**kwargskeyword argument list: keyword arguments passed directly to weights.W

__init__(coordinates, **kwargs)[source]¶

Methods

`__init__`(coordinates, **kwargs)
`asymmetry`([intrinsic])	Asymmetry check.
`from_WSP`(WSP[, silence_warnings])	Create a pysal W from a pysal WSP object (thin weights matrix).
`from_adjlist`(adjlist[, focal_col, ...])	Return an adjacency list representation of a weights object.
`from_dataframe`(df[, geom_col, ids, use_index])	Construct a Delaunay triangulation from a geopandas GeoDataFrame.
`from_file`([path, format])	Read a weights file into a W object.
`from_networkx`(graph[, weight_col])	Convert a `networkx` graph to a PySAL `W` object.
`from_shapefile`(args, *kwargs)
`from_sparse`(sparse)	Convert a `scipy.sparse` array to a PySAL `W` object.
`full`()	Generate a full `numpy.ndarray`.
`get_transform`()	Getter for transform property.
`plot`(gdf[, indexed_on, ax, color, node_kws, ...])	Plot spatial weights objects.
`remap_ids`(new_ids)	In place modification throughout `W` of id values from `w.id_order` to `new_ids` in all.
`set_shapefile`(shapefile[, idVariable, full])	Adding metadata for writing headers of `.gal` and `.gwt` files.
`set_transform`([value])	Transformations of weights.
`symmetrize`([inplace])	Construct a symmetric KNN weight.
`to_WSP`()	Generate a `WSP` object.
`to_adjlist`([remove_symmetric, drop_islands, ...])	Compute an adjacency list representation of a weights object.
`to_file`([path, format])	Write a weights to a file.
`to_networkx`()	Convert a weights object to a `networkx` graph.
`to_sparse`([fmt])	Generate a `scipy.sparse` array object from a pysal W.

Attributes

`asymmetries`	List of id pairs with asymmetric weights sorted in ascending index location order.
`cardinalities`	Number of neighbors for each observation.
`component_labels`	Store the graph component in which each observation falls.
`diagW2`	Diagonal of \(WW\).
`diagWtW`	Diagonal of \(W^{'}W\).
`diagWtW_WW`	Diagonal of \(W^{'}W + WW\).
`histogram`	Cardinality histogram as a dictionary where key is the id and value is the number of neighbors for that unit.
`id2i`	Dictionary where the key is an ID and the value is that ID's index in `W.id_order`.
`id_order`	Returns the ids for the observations in the order in which they would be encountered if iterating over the weights.
`id_order_set`	Returns `True` if user has set `id_order`, `False` if not.
`islands`	List of ids without any neighbors.
`max_neighbors`	Largest number of neighbors.
`mean_neighbors`	Average number of neighbors.
`min_neighbors`	Minimum number of neighbors.
`n`	Number of units.
`n_components`	Store whether the adjacency matrix is fully connected.
`neighbor_offsets`	Given the current `id_order`, `neighbor_offsets[id]` is the offsets of the id's neighbors in `id_order`.
`nonzero`	Number of nonzero weights.
`pct_nonzero`	Percentage of nonzero weights.
`s0`	`s0` is defined as
`s1`	`s1` is defined as
`s2`	`s2` is defined as
`s2array`	Individual elements comprising `s2`.
`sd`	Standard deviation of number of neighbors.
`sparse`	Sparse matrix object.
`transform`	Getter for transform property.
`trcW2`	Trace of \(WW\).
`trcWtW`	Trace of \(W^{'}W\).
`trcWtW_WW`	Trace of \(W^{'}W + WW\).