"""
Functions for constructing matrix-like objects from graph attributes.
"""
__all__ = ['attr_matrix', 'attr_sparse_matrix']
import networkx as nx
def _node_value(G, node_attr):
"""Returns a function that returns a value from G.nodes[u].
We return a function expecting a node as its sole argument. Then, in the
simplest scenario, the returned function will return G.nodes[u][node_attr].
However, we also handle the case when `node_attr` is None or when it is a
function itself.
Parameters
----------
G : graph
A NetworkX graph
node_attr : {None, str, callable}
Specification of how the value of the node attribute should be obtained
from the node attribute dictionary.
Returns
-------
value : function
A function expecting a node as its sole argument. The function will
returns a value from G.nodes[u] that depends on `edge_attr`.
"""
if node_attr is None:
def value(u): return u
elif not hasattr(node_attr, '__call__'):
# assume it is a key for the node attribute dictionary
def value(u): return G.nodes[u][node_attr]
else:
# Advanced: Allow users to specify something else.
#
# For example,
# node_attr = lambda u: G.nodes[u].get('size', .5) * 3
#
value = node_attr
return value
def _edge_value(G, edge_attr):
"""Returns a function that returns a value from G[u][v].
Suppose there exists an edge between u and v. Then we return a function
expecting u and v as arguments. For Graph and DiGraph, G[u][v] is
the edge attribute dictionary, and the function (essentially) returns
G[u][v][edge_attr]. However, we also handle cases when `edge_attr` is None
and when it is a function itself. For MultiGraph and MultiDiGraph, G[u][v]
is a dictionary of all edges between u and v. In this case, the returned
function sums the value of `edge_attr` for every edge between u and v.
Parameters
----------
G : graph
A NetworkX graph
edge_attr : {None, str, callable}
Specification of how the value of the edge attribute should be obtained
from the edge attribute dictionary, G[u][v]. For multigraphs, G[u][v]
is a dictionary of all the edges between u and v. This allows for
special treatment of multiedges.
Returns
-------
value : function
A function expecting two nodes as parameters. The nodes should
represent the from- and to- node of an edge. The function will
return a value from G[u][v] that depends on `edge_attr`.
"""
if edge_attr is None:
# topological count of edges
if G.is_multigraph():
def value(u, v): return len(G[u][v])
else:
def value(u, v): return 1
elif not hasattr(edge_attr, '__call__'):
# assume it is a key for the edge attribute dictionary
if edge_attr == 'weight':
# provide a default value
if G.is_multigraph():
def value(u, v): return sum([d.get(edge_attr, 1) for d in G[u][v].values()])
else:
def value(u, v): return G[u][v].get(edge_attr, 1)
else:
# otherwise, the edge attribute MUST exist for each edge
if G.is_multigraph():
def value(u, v): return sum([d[edge_attr] for d in G[u][v].values()])
else:
def value(u, v): return G[u][v][edge_attr]
else:
# Advanced: Allow users to specify something else.
#
# Alternative default value:
# edge_attr = lambda u,v: G[u][v].get('thickness', .5)
#
# Function on an attribute:
# edge_attr = lambda u,v: abs(G[u][v]['weight'])
#
# Handle Multi(Di)Graphs differently:
# edge_attr = lambda u,v: numpy.prod([d['size'] for d in G[u][v].values()])
#
# Ignore multiple edges
# edge_attr = lambda u,v: 1 if len(G[u][v]) else 0
#
value = edge_attr
return value
[docs]def attr_matrix(G, edge_attr=None, node_attr=None, normalized=False,
rc_order=None, dtype=None, order=None):
"""Returns a NumPy matrix using attributes from G.
If only `G` is passed in, then the adjacency matrix is constructed.
Let A be a discrete set of values for the node attribute `node_attr`. Then
the elements of A represent the rows and columns of the constructed matrix.
Now, iterate through every edge e=(u,v) in `G` and consider the value
of the edge attribute `edge_attr`. If ua and va are the values of the
node attribute `node_attr` for u and v, respectively, then the value of
the edge attribute is added to the matrix element at (ua, va).
Parameters
----------
G : graph
The NetworkX graph used to construct the NumPy matrix.
edge_attr : str, optional
Each element of the matrix represents a running total of the
specified edge attribute for edges whose node attributes correspond
to the rows/cols of the matirx. The attribute must be present for
all edges in the graph. If no attribute is specified, then we
just count the number of edges whose node attributes correspond
to the matrix element.
node_attr : str, optional
Each row and column in the matrix represents a particular value
of the node attribute. The attribute must be present for all nodes
in the graph. Note, the values of this attribute should be reliably
hashable. So, float values are not recommended. If no attribute is
specified, then the rows and columns will be the nodes of the graph.
normalized : bool, optional
If True, then each row is normalized by the summation of its values.
rc_order : list, optional
A list of the node attribute values. This list specifies the ordering
of rows and columns of the array. If no ordering is provided, then
the ordering will be random (and also, a return value).
Other Parameters
----------------
dtype : NumPy data-type, optional
A valid NumPy dtype used to initialize the array. Keep in mind certain
dtypes can yield unexpected results if the array is to be normalized.
The parameter is passed to numpy.zeros(). If unspecified, the NumPy
default is used.
order : {'C', 'F'}, optional
Whether to store multidimensional data in C- or Fortran-contiguous
(row- or column-wise) order in memory. This parameter is passed to
numpy.zeros(). If unspecified, the NumPy default is used.
Returns
-------
M : NumPy matrix
The attribute matrix.
ordering : list
If `rc_order` was specified, then only the matrix is returned.
However, if `rc_order` was None, then the ordering used to construct
the matrix is returned as well.
Examples
--------
Construct an adjacency matrix:
>>> G = nx.Graph()
>>> G.add_edge(0, 1, thickness=1, weight=3)
>>> G.add_edge(0, 2, thickness=2)
>>> G.add_edge(1, 2, thickness=3)
>>> nx.attr_matrix(G, rc_order=[0, 1, 2])
matrix([[0., 1., 1.],
[1., 0., 1.],
[1., 1., 0.]])
Alternatively, we can obtain the matrix describing edge thickness.
>>> nx.attr_matrix(G, edge_attr='thickness', rc_order=[0, 1, 2])
matrix([[0., 1., 2.],
[1., 0., 3.],
[2., 3., 0.]])
We can also color the nodes and ask for the probability distribution over
all edges (u,v) describing:
Pr(v has color Y | u has color X)
>>> G.nodes[0]['color'] = 'red'
>>> G.nodes[1]['color'] = 'red'
>>> G.nodes[2]['color'] = 'blue'
>>> rc = ['red', 'blue']
>>> nx.attr_matrix(G, node_attr='color', normalized=True, rc_order=rc)
matrix([[0.33333333, 0.66666667],
[1. , 0. ]])
For example, the above tells us that for all edges (u,v):
Pr( v is red | u is red) = 1/3
Pr( v is blue | u is red) = 2/3
Pr( v is red | u is blue) = 1
Pr( v is blue | u is blue) = 0
Finally, we can obtain the total weights listed by the node colors.
>>> nx.attr_matrix(G, edge_attr='weight', node_attr='color', rc_order=rc)
matrix([[3., 2.],
[2., 0.]])
Thus, the total weight over all edges (u,v) with u and v having colors:
(red, red) is 3 # the sole contribution is from edge (0,1)
(red, blue) is 2 # contributions from edges (0,2) and (1,2)
(blue, red) is 2 # same as (red, blue) since graph is undirected
(blue, blue) is 0 # there are no edges with blue endpoints
"""
try:
import numpy as np
except ImportError:
raise ImportError(
"attr_matrix() requires numpy: http://scipy.org/ ")
edge_value = _edge_value(G, edge_attr)
node_value = _node_value(G, node_attr)
if rc_order is None:
ordering = list(set([node_value(n) for n in G]))
else:
ordering = rc_order
N = len(ordering)
undirected = not G.is_directed()
index = dict(zip(ordering, range(N)))
M = np.zeros((N, N), dtype=dtype, order=order)
seen = set([])
for u, nbrdict in G.adjacency():
for v in nbrdict:
# Obtain the node attribute values.
i, j = index[node_value(u)], index[node_value(v)]
if v not in seen:
M[i, j] += edge_value(u, v)
if undirected:
M[j, i] = M[i, j]
if undirected:
seen.add(u)
if normalized:
M /= M.sum(axis=1).reshape((N, 1))
M = np.asmatrix(M)
if rc_order is None:
return M, ordering
else:
return M
[docs]def attr_sparse_matrix(G, edge_attr=None, node_attr=None,
normalized=False, rc_order=None, dtype=None):
"""Returns a SciPy sparse matrix using attributes from G.
If only `G` is passed in, then the adjacency matrix is constructed.
Let A be a discrete set of values for the node attribute `node_attr`. Then
the elements of A represent the rows and columns of the constructed matrix.
Now, iterate through every edge e=(u,v) in `G` and consider the value
of the edge attribute `edge_attr`. If ua and va are the values of the
node attribute `node_attr` for u and v, respectively, then the value of
the edge attribute is added to the matrix element at (ua, va).
Parameters
----------
G : graph
The NetworkX graph used to construct the NumPy matrix.
edge_attr : str, optional
Each element of the matrix represents a running total of the
specified edge attribute for edges whose node attributes correspond
to the rows/cols of the matirx. The attribute must be present for
all edges in the graph. If no attribute is specified, then we
just count the number of edges whose node attributes correspond
to the matrix element.
node_attr : str, optional
Each row and column in the matrix represents a particular value
of the node attribute. The attribute must be present for all nodes
in the graph. Note, the values of this attribute should be reliably
hashable. So, float values are not recommended. If no attribute is
specified, then the rows and columns will be the nodes of the graph.
normalized : bool, optional
If True, then each row is normalized by the summation of its values.
rc_order : list, optional
A list of the node attribute values. This list specifies the ordering
of rows and columns of the array. If no ordering is provided, then
the ordering will be random (and also, a return value).
Other Parameters
----------------
dtype : NumPy data-type, optional
A valid NumPy dtype used to initialize the array. Keep in mind certain
dtypes can yield unexpected results if the array is to be normalized.
The parameter is passed to numpy.zeros(). If unspecified, the NumPy
default is used.
Returns
-------
M : SciPy sparse matrix
The attribute matrix.
ordering : list
If `rc_order` was specified, then only the matrix is returned.
However, if `rc_order` was None, then the ordering used to construct
the matrix is returned as well.
Examples
--------
Construct an adjacency matrix:
>>> G = nx.Graph()
>>> G.add_edge(0,1,thickness=1,weight=3)
>>> G.add_edge(0,2,thickness=2)
>>> G.add_edge(1,2,thickness=3)
>>> M = nx.attr_sparse_matrix(G, rc_order=[0,1,2])
>>> M.todense()
matrix([[0., 1., 1.],
[1., 0., 1.],
[1., 1., 0.]])
Alternatively, we can obtain the matrix describing edge thickness.
>>> M = nx.attr_sparse_matrix(G, edge_attr='thickness', rc_order=[0,1,2])
>>> M.todense()
matrix([[0., 1., 2.],
[1., 0., 3.],
[2., 3., 0.]])
We can also color the nodes and ask for the probability distribution over
all edges (u,v) describing:
Pr(v has color Y | u has color X)
>>> G.nodes[0]['color'] = 'red'
>>> G.nodes[1]['color'] = 'red'
>>> G.nodes[2]['color'] = 'blue'
>>> rc = ['red', 'blue']
>>> M = nx.attr_sparse_matrix(G, node_attr='color', \
normalized=True, rc_order=rc)
>>> M.todense()
matrix([[0.33333333, 0.66666667],
[1. , 0. ]])
For example, the above tells us that for all edges (u,v):
Pr( v is red | u is red) = 1/3
Pr( v is blue | u is red) = 2/3
Pr( v is red | u is blue) = 1
Pr( v is blue | u is blue) = 0
Finally, we can obtain the total weights listed by the node colors.
>>> M = nx.attr_sparse_matrix(G, edge_attr='weight',\
node_attr='color', rc_order=rc)
>>> M.todense()
matrix([[3., 2.],
[2., 0.]])
Thus, the total weight over all edges (u,v) with u and v having colors:
(red, red) is 3 # the sole contribution is from edge (0,1)
(red, blue) is 2 # contributions from edges (0,2) and (1,2)
(blue, red) is 2 # same as (red, blue) since graph is undirected
(blue, blue) is 0 # there are no edges with blue endpoints
"""
try:
import numpy as np
from scipy import sparse
except ImportError:
raise ImportError(
"attr_sparse_matrix() requires scipy: http://scipy.org/ ")
edge_value = _edge_value(G, edge_attr)
node_value = _node_value(G, node_attr)
if rc_order is None:
ordering = list(set([node_value(n) for n in G]))
else:
ordering = rc_order
N = len(ordering)
undirected = not G.is_directed()
index = dict(zip(ordering, range(N)))
M = sparse.lil_matrix((N, N), dtype=dtype)
seen = set([])
for u, nbrdict in G.adjacency():
for v in nbrdict:
# Obtain the node attribute values.
i, j = index[node_value(u)], index[node_value(v)]
if v not in seen:
M[i, j] += edge_value(u, v)
if undirected:
M[j, i] = M[i, j]
if undirected:
seen.add(u)
if normalized:
norms = np.asarray(M.sum(axis=1)).ravel()
for i, norm in enumerate(norms):
M[i, :] /= norm
if rc_order is None:
return M, ordering
else:
return M
# fixture for pytest
def setup_module(module):
import pytest
numpy = pytest.importorskip('numpy')
scipy = pytest.importorskip('scipy')