libpysal.weights.W¶

class
libpysal.weights.
W
(neighbors, weights=None, id_order=None, silence_warnings=False, ids=None)[source]¶ Spatial weights class. Class attributes are described by their docstrings. to view, use the
help
function. Parameters
 neighbors
dict
Key is region ID, value is a list of neighbor IDS. For example,
{'a':['b'],'b':['a','c'],'c':['b']}
. weights
dict
Key is region ID, value is a list of edge weights. If not supplied all edge weights are assumed to have a weight of 1. For example,
{'a':[0.5],'b':[0.5,1.5],'c':[1.5]}
. id_order
list
An ordered list of ids, defines the order of observations when iterating over
W
if not set, lexicographical ordering is used to iterate and theid_order_set
property will returnFalse
. This can be set after creation by setting theid_order
property. silence_warningsbool
By default
libpysal
will print a warning if the dataset contains any disconnected components or islands. To silence this warning set this parameter toTrue
. ids
list
Values to use for keys of the neighbors and weights
dict
objects.
 neighbors
Examples
>>> from libpysal.weights import W >>> neighbors = {0: [3, 1], 1: [0, 4, 2], 2: [1, 5], 3: [0, 6, 4], 4: [1, 3, 7, 5], 5: [2, 4, 8], 6: [3, 7], 7: [4, 6, 8], 8: [5, 7]} >>> weights = {0: [1, 1], 1: [1, 1, 1], 2: [1, 1], 3: [1, 1, 1], 4: [1, 1, 1, 1], 5: [1, 1, 1], 6: [1, 1], 7: [1, 1, 1], 8: [1, 1]} >>> w = W(neighbors, weights) >>> "%.3f"%w.pct_nonzero '29.630'
Read from external .gal file.
>>> import libpysal >>> w = libpysal.io.open(libpysal.examples.get_path("stl.gal")).read() >>> w.n 78 >>> "%.3f"%w.pct_nonzero '6.542'
Set weights implicitly.
>>> neighbors = {0: [3, 1], 1: [0, 4, 2], 2: [1, 5], 3: [0, 6, 4], 4: [1, 3, 7, 5], 5: [2, 4, 8], 6: [3, 7], 7: [4, 6, 8], 8: [5, 7]} >>> w = W(neighbors) >>> round(w.pct_nonzero,3) 29.63 >>> from libpysal.weights import lat2W >>> w = lat2W(100, 100) >>> w.trcW2 39600.0 >>> w.trcWtW 39600.0 >>> w.transform='r' >>> round(w.trcW2, 3) 2530.722 >>> round(w.trcWtW, 3) 2533.667
Cardinality Histogram:
>>> w.histogram [(2, 4), (3, 392), (4, 9604)]
Disconnected observations (islands):
>>> from libpysal.weights import W >>> w = W({1:[0],0:[1],2:[], 3:[]})
UserWarning: The weights matrix is not fully connected: There are 3 disconnected components. There are 2 islands with ids: 2, 3.
 Attributes
asymmetries
List of id pairs with asymmetric weights.
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 setid_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 inid_order
.nonzero
Number of nonzero weights.
pct_nonzero
Percentage of nonzero weights.
s0
s0
is defined ass1
s1
is defined ass2
s2
is defined ass2array
Individual elements comprising
s2
.sd
Standard deviation of number of neighbors.
sparse
Sparse matrix object.
trcW2
Trace of \(WW\).
trcWtW
Trace of \(W^{'}W\).
trcWtW_WW
Trace of \(W^{'}W + WW\).
transform
Getter for transform property.

__init__
(self, neighbors, weights=None, id_order=None, silence_warnings=False, ids=None)[source]¶ Initialize self. See help(type(self)) for accurate signature.
Methods
__init__
(self, neighbors[, weights, …])Initialize self.
asymmetry
(self[, intrinsic])Asymmetry check.
from_WSP
(WSP[, silence_warnings])from_adjlist
(adjlist[, focal_col, …])Return an adjacency list representation of a weights object.
from_file
([path, format])Read a weights file into a W object.
from_networkx
(graph[, weight_col])Convert a
networkx
graph to a PySALW
object.from_shapefile
(\*args, \*\*kwargs)full
(self)Generate a full
numpy.ndarray
.get_transform
(self)Getter for transform property.
plot
(self, gdf[, indexed_on, ax, color, …])Plot spatial weights objects.
remap_ids
(self, new_ids)In place modification throughout
W
of id values fromw.id_order
tonew_ids
in all.set_shapefile
(self, shapefile[, idVariable, …])Adding metadata for writing headers of
.gal
and.gwt
files.set_transform
(self[, value])Transformations of weights.
symmetrize
(self[, inplace])Construct a symmetric KNN weight.
to_WSP
(self)Generate a
WSP
object.to_adjlist
(self[, remove_symmetric, …])Compute an adjacency list representation of a weights object.
to_file
(self[, path, format])Write a weights to a file.
to_networkx
(self)Convert a weights object to a
networkx
graph.Attributes
List of id pairs with asymmetric weights.
Number of neighbors for each observation.
Store the graph component in which each observation falls.
Diagonal of \(WW\).
Diagonal of \(W^{'}W\).
Diagonal of \(W^{'}W + WW\).
Cardinality histogram as a dictionary where key is the id and value is the number of neighbors for that unit.
Dictionary where the key is an ID and the value is that ID’s index in
W.id_order
.Returns the ids for the observations in the order in which they would be encountered if iterating over the weights.
Returns
True
if user has setid_order
,False
if not.List of ids without any neighbors.
Largest number of neighbors.
Average number of neighbors.
Minimum number of neighbors.
Number of units.
Store whether the adjacency matrix is fully connected.
Given the current
id_order
,neighbor_offsets[id]
is the offsets of the id’s neighbors inid_order
.Number of nonzero weights.
Percentage of nonzero weights.
s0
is defined ass1
is defined ass2
is defined asIndividual elements comprising
s2
.Standard deviation of number of neighbors.
Sparse matrix object.
Getter for transform property.
Trace of \(WW\).
Trace of \(W^{'}W\).
Trace of \(W^{'}W + WW\).

property
asymmetries
¶ List of id pairs with asymmetric weights.

asymmetry
(self, intrinsic=True)[source]¶ Asymmetry check.
 Parameters
 intrinsicbool
Default is
True
. Intrinsic symmetry is defined as\[w_{i,j} == w_{j,i}\]If
intrinsic
isFalse
symmetry is defined as\[i \in N_j \ \& \ j \in N_i\]where \(N_j\) is the set of neighbors for \(j\).
 Returns
 asymmetries
list
Empty if no asymmetries are found if asymmetries, then a
list
of(i,j)
tuples is returned.
 asymmetries
Examples
>>> from libpysal.weights import lat2W >>> w=lat2W(3,3) >>> w.asymmetry() [] >>> w.transform='r' >>> w.asymmetry() [(0, 1), (0, 3), (1, 0), (1, 2), (1, 4), (2, 1), (2, 5), (3, 0), (3, 4), (3, 6), (4, 1), (4, 3), (4, 5), (4, 7), (5, 2), (5, 4), (5, 8), (6, 3), (6, 7), (7, 4), (7, 6), (7, 8), (8, 5), (8, 7)] >>> result = w.asymmetry(intrinsic=False) >>> result [] >>> neighbors={0:[1,2,3], 1:[1,2,3], 2:[0,1], 3:[0,1]} >>> weights={0:[1,1,1], 1:[1,1,1], 2:[1,1], 3:[1,1]} >>> w=W(neighbors,weights) >>> w.asymmetry() [(0, 1), (1, 0)]

property
cardinalities
¶ Number of neighbors for each observation.

property
component_labels
¶ Store the graph component in which each observation falls.

property
diagWtW_WW
¶ Diagonal of \(W^{'}W + WW\).

classmethod
from_adjlist
(adjlist, focal_col='focal', neighbor_col='neighbor', weight_col=None)[source]¶ Return an adjacency list representation of a weights object.
 Parameters
 adjlist
pandas.DataFrame
Adjacency list with a minimum of two columns.
 focal_col
str
Name of the column with the “source” node ids.
 neighbor_col
str
Name of the column with the “destination” node ids.
 weight_col
str
Name of the column with the weight information. If not provided and the dataframe has no column named “weight” then all weights are assumed to be 1.
 adjlist

classmethod
from_networkx
(graph, weight_col='weight')[source]¶ Convert a
networkx
graph to a PySALW
object. Parameters
 graph
networkx.Graph
The graph to convert to a
W
. weight_col
str
If the graph is labeled, this should be the name of the field to use as the weight for the
W
.
 graph
 Returns
 w
libpysal.weights.W
A
W
object containing the same graph as thenetworkx
graph.
 w

full
(self)[source]¶ Generate a full
numpy.ndarray
. Parameters
 self
libpysal.weights.W
spatial weights object
 self
 Returns
 (fullw, keys)
tuple
The first element being the full
numpy.ndarray
and second element keys being the ids associated with each row in the array.
 (fullw, keys)
Examples
>>> from libpysal.weights import W, full >>> neighbors = {'first':['second'],'second':['first','third'],'third':['second']} >>> weights = {'first':[1],'second':[1,1],'third':[1]} >>> w = W(neighbors, weights) >>> wf, ids = full(w) >>> wf array([[0., 1., 0.], [1., 0., 1.], [0., 1., 0.]]) >>> ids ['first', 'second', 'third']

get_transform
(self)[source]¶ Getter for transform property.
 Returns
See also
Examples
>>> from libpysal.weights import lat2W >>> w=lat2W() >>> w.weights[0] [1.0, 1.0] >>> w.transform 'O' >>> w.transform='r' >>> w.weights[0] [0.5, 0.5] >>> w.transform='b' >>> w.weights[0] [1.0, 1.0]

property
histogram
¶ Cardinality histogram as a dictionary where key is the id and value is the number of neighbors for that unit.

property
id2i
¶ Dictionary where the key is an ID and the value is that ID’s index in
W.id_order
.

property
id_order
¶ Returns the ids for the observations in the order in which they would be encountered if iterating over the weights.

property
id_order_set
¶ Returns
True
if user has setid_order
,False
if not.Examples
>>> from libpysal.weights import lat2W >>> w=lat2W() >>> w.id_order_set True

property
islands
¶ List of ids without any neighbors.

property
max_neighbors
¶ Largest number of neighbors.

property
mean_neighbors
¶ Average number of neighbors.

property
min_neighbors
¶ Minimum number of neighbors.

property
n
¶ Number of units.

property
n_components
¶ Store whether the adjacency matrix is fully connected.

property
neighbor_offsets
¶ Given the current
id_order
,neighbor_offsets[id]
is the offsets of the id’s neighbors inid_order
. Returns
 neighbor_list
list
Offsets of the id’s neighbors in
id_order
.
 neighbor_list
Examples
>>> from libpysal.weights import W >>> neighbors={'c': ['b'], 'b': ['c', 'a'], 'a': ['b']} >>> weights ={'c': [1.0], 'b': [1.0, 1.0], 'a': [1.0]} >>> w=W(neighbors,weights) >>> w.id_order = ['a','b','c'] >>> w.neighbor_offsets['b'] [2, 0] >>> w.id_order = ['b','a','c'] >>> w.neighbor_offsets['b'] [2, 1]

property
nonzero
¶ Number of nonzero weights.

property
pct_nonzero
¶ Percentage of nonzero weights.

plot
(self, gdf, indexed_on=None, ax=None, color='k', node_kws=None, edge_kws=None)[source]¶ Plot spatial weights objects. Requires
matplotlib
, and implicitly requires ageopandas.GeoDataFrame
as input. Parameters
 gdf
geopandas.GeoDataFrame
The original shapes whose topological relations are modelled in
W
. indexed_on
str
Column of
geopandas.GeoDataFrame
that the weights object uses as an index. Default isNone
, so the index of thegeopandas.GeoDataFrame
is used. ax
matplotlib.axes.Axes
Axis on which to plot the weights. Default is
None
, so plots on the current figure. color
str
matplotlib
color string, will color both nodes and edges the same by default. node_kws
dict
Keyword arguments dictionary to send to
pyplot.scatter
, which provides finegrained control over the aesthetics of the nodes in the plot. edge_kws
dict
Keyword arguments dictionary to send to
pyplot.plot
, which provides finegrained control over the aesthetics of the edges in the plot.
 gdf
 Returns
 f
matplotlib.figure.Figure
Figure on which the plot is made.
 ax
matplotlib.axes.Axes
Axis on which the plot is made.
 f
Notes
If you’d like to overlay the actual shapes from the
geopandas.GeoDataFrame
, callgdf.plot(ax=ax)
after this. To plot underneath, adjust the zorder of the plot as follows:gdf.plot(ax=ax,zorder=0)
.Examples
>>> from libpysal.weights import Queen >>> import libpysal as lp >>> import geopandas >>> gdf = geopandas.read_file(lp.examples.get_path("columbus.shp")) >>> weights = Queen.from_dataframe(gdf) >>> tmp = weights.plot(gdf, color='firebrickred', node_kws=dict(marker='*', color='k'))

remap_ids
(self, new_ids)[source]¶ In place modification throughout
W
of id values fromw.id_order
tonew_ids
in all. Parameters
 new_ids
list
,numpy.ndarray
Aligned list of new ids to be inserted. Note that first element of
new_ids
will replace first element ofw.id_order
, second element ofnew_ids
replaces second element ofw.id_order
and so on.
 new_ids
Examples
>>> from libpysal.weights import lat2W >>> w = lat2W(3, 3) >>> w.id_order [0, 1, 2, 3, 4, 5, 6, 7, 8] >>> w.neighbors[0] [3, 1] >>> new_ids = ['id%i'%id for id in w.id_order] >>> _ = w.remap_ids(new_ids) >>> w.id_order ['id0', 'id1', 'id2', 'id3', 'id4', 'id5', 'id6', 'id7', 'id8'] >>> w.neighbors['id0'] ['id3', 'id1']

property
s0
¶ s0
is defined as\[s0=\sum_i \sum_j w_{i,j}\]

property
s1
¶ s1
is defined as\[s1=1/2 \sum_i \sum_j \Big(w_{i,j} + w_{j,i}\Big)^2\]

property
s2
¶ s2
is defined as\[s2=\sum_j \Big(\sum_i w_{i,j} + \sum_i w_{j,i}\Big)^2\]

property
sd
¶ Standard deviation of number of neighbors.

set_shapefile
(self, shapefile, idVariable=None, full=False)[source]¶ Adding metadata for writing headers of
.gal
and.gwt
files.

set_transform
(self, value='B')[source]¶ Transformations of weights.
 Parameters
 transform
str
This parameter is not case sensitive. The following are valid transformations.
B – Binary
R – Rowstandardization (global sum \(=n\))
D – Doublestandardization (global sum \(=1\))
V – Variance stabilizing
O – Restore original transformation (from instantiation)
 transform
Notes
Transformations are applied only to the value of the weights at instantiation. Chaining of transformations cannot be done on a
W
instance.Examples
>>> from libpysal.weights import lat2W >>> w=lat2W() >>> w.weights[0] [1.0, 1.0] >>> w.transform 'O' >>> w.transform='r' >>> w.weights[0] [0.5, 0.5] >>> w.transform='b' >>> w.weights[0] [1.0, 1.0]

property
sparse
¶ Sparse matrix object. For any matrix manipulations required for w,
w.sparse
should be used. This is based onscipy.sparse
.

symmetrize
(self, inplace=False)[source]¶ Construct a symmetric KNN weight. This ensures that the neighbors of each focal observation consider the focal observation itself as a neighbor. This returns a generic
W
object, since the object is no longer guaranteed to havek
neighbors for each observation.

to_WSP
(self)[source]¶ Generate a
WSP
object. Returns
 implicit
libpysal.weights.WSP
Thin
W
class
 implicit
See also
Examples
>>> from libpysal.weights import W, WSP >>> neighbors={'first':['second'],'second':['first','third'],'third':['second']} >>> weights={'first':[1],'second':[1,1],'third':[1]} >>> w=W(neighbors,weights) >>> wsp=w.to_WSP() >>> isinstance(wsp, WSP) True >>> wsp.n 3 >>> wsp.s0 4

to_adjlist
(self, remove_symmetric=False, focal_col='focal', neighbor_col='neighbor', weight_col='weight')[source]¶ Compute an adjacency list representation of a weights object.
 Parameters
 remove_symmetricbool
Whether or not to remove symmetric entries. If the
W
is symmetric, a standard directed adjacency list will contain both the forward and backward links by default because adjacency lists are a directed graph representation. If this isTrue
, aW
created from this adjacency list MAY NOT BE THE SAME as the originalW
. If you would like to consider (1,2) and (2,1) as distinct links, leave this asFalse
. focal_col
str
Name of the column in which to store “source” node ids.
 neighbor_col
str
Name of the column in which to store “destination” node ids.
 weight_col
str
Name of the column in which to store weight information.

to_file
(self, path='', format=None)[source]¶ Write a weights to a file. The format is guessed automatically from the path, but can be overridden with the format argument.
See libpysal.io.FileIO for more information.
 Returns

to_networkx
(self)[source]¶ Convert a weights object to a
networkx
graph. Returns
A
networkx
graph
representation
of
the
W
object.

property
transform
¶ Getter for transform property.
 Returns
See also
Examples
>>> from libpysal.weights import lat2W >>> w=lat2W() >>> w.weights[0] [1.0, 1.0] >>> w.transform 'O' >>> w.transform='r' >>> w.weights[0] [0.5, 0.5] >>> w.transform='b' >>> w.weights[0] [1.0, 1.0]

property
trcWtW_WW
¶ Trace of \(W^{'}W + WW\).