# libpysal.weights.Gabriel

class libpysal.weights.Gabriel(coordinates, **kwargs)

  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:

  1. Construct the circle C_ij containing link (i,j) as its diameter

  2. If any other node k is contained within C_ij, then remove link (i,j) from the graph.

  3. Once all links are evaluated, the remaining graph is the Gabriel graph.

  Parameters:
    coordinates `array` `of` `points`, (N,2)

      numpy array of coordinates containing locations to compute the delaunay triangulation

    **kwargs `keyword` `argument` `python:list`

      keyword arguments passed directly to weights.W

  __init__(coordinates, **kwargs)

  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 \(W^{'}W + WW\).