def random_layout(G, center=None, dim=2, random_state=None):
"""Position nodes uniformly at random in the unit square.
For every node, a position is generated by choosing each of dim
coordinates uniformly at random on the interval [0.0, 1.0).
NumPy (http://scipy.org) is required for this function.
Parameters
----------
G : NetworkX graph or list of nodes
A position will be assigned to every node in G.
center : array-like or None
Coordinate pair around which to center the layout.
dim : int
Dimension of layout.
random_state : int, RandomState instance or None optional (default=None)
Set the random state for deterministic node layouts.
If int, `random_state` is the seed used by the random number generator,
if numpy.random.RandomState instance, `random_state` is the random
number generator,
if None, the random number generator is the RandomState instance used
by numpy.random.
Returns
-------
pos : dict
A dictionary of positions keyed by node
Examples
--------
>>> G = nx.lollipop_graph(4, 3)
>>> pos = nx.random_layout(G)
"""
import numpy as np
G, center = _process_params(G, center, dim)
shape = (len(G), dim)
pos = random_state.rand(*shape) + center
pos = pos.astype(np.float32)
pos = dict(zip(G, pos))
return pos
def random_layout(G, center=None, dim=2, random_state=None):
"""Position nodes uniformly at random in the unit square.
For every node, a position is generated by choosing each of dim
coordinates uniformly at random on the interval [0.0, 1.0).
NumPy (http://scipy.org) is required for this function.
Parameters
----------
G : NetworkX graph or list of nodes
A position will be assigned to every node in G.
center : array-like or None
Coordinate pair around which to center the layout.
dim : int
Dimension of layout.
random_state : int, RandomState instance or None optional (default=None)
Set the random state for deterministic node layouts.
If int, `random_state` is the seed used by the random number generator,
if numpy.random.RandomState instance, `random_state` is the random
number generator,
if None, the random number generator is the RandomState instance used
by numpy.random.
Returns
-------
pos : dict
A dictionary of positions keyed by node
Examples
--------
>>> G = nx.lollipop_graph(4, 3)
>>> pos = nx.random_layout(G)
"""
import numpy as np
G, center = _process_params(G, center, dim)
shape = (len(G), dim)
pos = random_state.rand(*shape) + center
pos = pos.astype(np.float32)
pos = dict(zip(G, pos))
return pos
def _sparse_fruchterman_reingold(A, k=None, pos=None, fixed=None,
iterations=50, threshold=1e-4, dim=2,
random_state=None):
# Position nodes in adjacency matrix A using Fruchterman-Reingold
# Entry point for NetworkX graph is fruchterman_reingold_layout()
# Sparse version
try:
import numpy as np
except ImportError:
m = "_sparse_fruchterman_reingold() requires numpy: http://scipy.org/"
raise ImportError(m)
try:
nnodes, _ = A.shape
except AttributeError:
msg = "fruchterman_reingold() takes an adjacency matrix as input"
raise nx.NetworkXError(msg)
try:
from scipy.sparse import spdiags, coo_matrix
except ImportError:
msg = "_sparse_fruchterman_reingold() scipy numpy: http://scipy.org/ "
raise ImportError(msg)
# make sure we have a LIst of Lists representation
try:
A = A.tolil()
except:
A = (coo_matrix(A)).tolil()
if pos is None:
# random initial positions
pos = np.asarray(random_state.rand(nnodes, dim), dtype=A.dtype)
else:
# make sure positions are of same type as matrix
pos = pos.astype(A.dtype)
# no fixed nodes
if fixed is None:
fixed = []
# optimal distance between nodes
if k is None:
k = np.sqrt(1.0 / nnodes)
# the initial "temperature" is about .1 of domain area (=1x1)
# this is the largest step allowed in the dynamics.
t = max(max(pos.T[0]) - min(pos.T[0]), max(pos.T[1]) - min(pos.T[1])) * 0.1
# simple cooling scheme.
# linearly step down by dt on each iteration so last iteration is size dt.
dt = t / float(iterations + 1)
displacement = np.zeros((dim, nnodes))
for iteration in range(iterations):
displacement *= 0
# loop over rows
for i in range(A.shape[0]):
if i in fixed:
continue
# difference between this row's node position and all others
delta = (pos[i] - pos).T
# distance between points
distance = np.sqrt((delta**2).sum(axis=0))
# enforce minimum distance of 0.01
distance = np.where(distance < 0.01, 0.01, distance)
# the adjacency matrix row
Ai = np.asarray(A.getrowview(i).toarray())
# displacement "force"
displacement[:, i] +=\
(delta * (k * k / distance**2 - Ai * distance / k)).sum(axis=1)
# update positions
length = np.sqrt((displacement**2).sum(axis=0))
length = np.where(length < 0.01, 0.1, length)
delta_pos = (displacement * t / length).T
pos += delta_pos
# cool temperature
t -= dt
err = np.linalg.norm(delta_pos) / nnodes
if err < threshold:
break
return pos
def _fruchterman_reingold(A, k=None, pos=None, fixed=None, iterations=50,
threshold=1e-4, dim=2, random_state=None):
# Position nodes in adjacency matrix A using Fruchterman-Reingold
# Entry point for NetworkX graph is fruchterman_reingold_layout()
try:
import numpy as np
except ImportError:
msg = "_fruchterman_reingold() requires numpy: http://scipy.org/ "
raise ImportError(msg)
try:
nnodes, _ = A.shape
except AttributeError:
msg = "fruchterman_reingold() takes an adjacency matrix as input"
raise nx.NetworkXError(msg)
# make sure we have an array instead of a matrix
A = np.asarray(A)
if pos is None:
# random initial positions
pos = np.asarray(random_state.rand(nnodes, dim), dtype=A.dtype)
else:
# make sure positions are of same type as matrix
pos = pos.astype(A.dtype)
# optimal distance between nodes
if k is None:
k = np.sqrt(1.0 / nnodes)
# the initial "temperature" is about .1 of domain area (=1x1)
# this is the largest step allowed in the dynamics.
# We need to calculate this in case our fixed positions force our domain
# to be much bigger than 1x1
t = max(max(pos.T[0]) - min(pos.T[0]), max(pos.T[1]) - min(pos.T[1])) * 0.1
# simple cooling scheme.
# linearly step down by dt on each iteration so last iteration is size dt.
dt = t / float(iterations + 1)
delta = np.zeros((pos.shape[0], pos.shape[0], pos.shape[1]), dtype=A.dtype)
# the inscrutable (but fast) version
# this is still O(V^2)
# could use multilevel methods to speed this up significantly
for iteration in range(iterations):
# matrix of difference between points
delta = pos[:, np.newaxis, :] - pos[np.newaxis, :, :]
# distance between points
distance = np.linalg.norm(delta, axis=-1)
# enforce minimum distance of 0.01
np.clip(distance, 0.01, None, out=distance)
# displacement "force"
displacement = np.einsum('ijk,ij->ik',
delta,
(k * k / distance**2 - A * distance / k))
# update positions
length = np.linalg.norm(displacement, axis=-1)
length = np.where(length < 0.01, 0.1, length)
delta_pos = np.einsum('ij,i->ij', displacement, t / length)
if fixed is not None:
# don't change positions of fixed nodes
delta_pos[fixed] = 0.0
pos += delta_pos
# cool temperature
t -= dt
err = np.linalg.norm(delta_pos) / nnodes
if err < threshold:
break
return pos
def fruchterman_reingold_layout(G,
k=None,
pos=None,
fixed=None,
iterations=50,
threshold=1e-4,
weight='weight',
scale=1,
center=None,
dim=2,
random_state=None):
"""Position nodes using Fruchterman-Reingold force-directed algorithm.
Parameters
----------
G : NetworkX graph or list of nodes
A position will be assigned to every node in G.
k : float (default=None)
Optimal distance between nodes. If None the distance is set to
1/sqrt(n) where n is the number of nodes. Increase this value
to move nodes farther apart.
pos : dict or None optional (default=None)
Initial positions for nodes as a dictionary with node as keys
and values as a coordinate list or tuple. If None, then use
random initial positions.
fixed : list or None optional (default=None)
Nodes to keep fixed at initial position.
iterations : int optional (default=50)
Maximum number of iterations taken
threshold: float optional (default = 1e-4)
Threshold for relative error in node position changes.
The iteration stops if the error is below this threshold.
weight : string or None optional (default='weight')
The edge attribute that holds the numerical value used for
the edge weight. If None, then all edge weights are 1.
scale : number (default: 1)
Scale factor for positions. Not used unless `fixed is None`.
center : array-like or None
Coordinate pair around which to center the layout.
Not used unless `fixed is None`.
dim : int
Dimension of layout.
random_state : int, RandomState instance or None optional (default=None)
Set the random state for deterministic node layouts.
If int, `random_state` is the seed used by the random number generator,
if numpy.random.RandomState instance, `random_state` is the random
number generator,
if None, the random number generator is the RandomState instance used
by numpy.random.
Returns
-------
pos : dict
A dictionary of positions keyed by node
Examples
--------
>>> G = nx.path_graph(4)
>>> pos = nx.spring_layout(G)
# The same using longer but equivalent function name
>>> pos = nx.fruchterman_reingold_layout(G)
"""
import numpy as np
G, center = _process_params(G, center, dim)
if fixed is not None:
nfixed = dict(zip(G, range(len(G))))
fixed = np.asarray([nfixed[v] for v in fixed])
if pos is not None:
# Determine size of existing domain to adjust initial positions
dom_size = max(coord for pos_tup in pos.values() for coord in pos_tup)
if dom_size == 0:
dom_size = 1
shape = (len(G), dim)
pos_arr = random_state.rand(*shape) * dom_size + center
for i, n in enumerate(G):
if n in pos:
pos_arr[i] = np.asarray(pos[n])
else:
pos_arr = None
if len(G) == 0:
return {}
if len(G) == 1:
return {nx.utils.arbitrary_element(G.nodes()): center}
try:
# Sparse matrix
if len(G) < 500: # sparse solver for large graphs
raise ValueError
A = nx.to_scipy_sparse_matrix(G, weight=weight, dtype='f')
if k is None and fixed is not None:
# We must adjust k by domain size for layouts not near 1x1
nnodes, _ = A.shape
k = dom_size / np.sqrt(nnodes)
pos = _sparse_fruchterman_reingold(A, k, pos_arr, fixed,
iterations, threshold,
dim, random_state)
except:
A = nx.to_numpy_matrix(G, weight=weight)
if k is None and fixed is not None:
# We must adjust k by domain size for layouts not near 1x1
nnodes, _ = A.shape
k = dom_size / np.sqrt(nnodes)
pos = _fruchterman_reingold(A, k, pos_arr, fixed, iterations,
threshold, dim, random_state)
if fixed is None:
pos = rescale_layout(pos, scale=scale) + center
pos = dict(zip(G, pos))
return pos
def _sparse_fruchterman_reingold(A, k=None, pos=None, fixed=None,
iterations=50, threshold=1e-4, dim=2,
random_state=None):
# Position nodes in adjacency matrix A using Fruchterman-Reingold
# Entry point for NetworkX graph is fruchterman_reingold_layout()
# Sparse version
try:
import numpy as np
except ImportError:
m = "_sparse_fruchterman_reingold() requires numpy: http://scipy.org/"
raise ImportError(m)
try:
nnodes, _ = A.shape
except AttributeError:
msg = "fruchterman_reingold() takes an adjacency matrix as input"
raise nx.NetworkXError(msg)
try:
from scipy.sparse import spdiags, coo_matrix
except ImportError:
msg = "_sparse_fruchterman_reingold() scipy numpy: http://scipy.org/ "
raise ImportError(msg)
# make sure we have a LIst of Lists representation
try:
A = A.tolil()
except:
A = (coo_matrix(A)).tolil()
if pos is None:
# random initial positions
pos = np.asarray(random_state.rand(nnodes, dim), dtype=A.dtype)
else:
# make sure positions are of same type as matrix
pos = pos.astype(A.dtype)
# no fixed nodes
if fixed is None:
fixed = []
# optimal distance between nodes
if k is None:
k = np.sqrt(1.0/nnodes)
# the initial "temperature" is about .1 of domain area (=1x1)
# this is the largest step allowed in the dynamics.
t = 0.1
# simple cooling scheme.
# linearly step down by dt on each iteration so last iteration is size dt.
dt = t / float(iterations+1)
displacement = np.zeros((dim, nnodes))
for iteration in range(iterations):
displacement *= 0
# loop over rows
for i in range(A.shape[0]):
if i in fixed:
continue
# difference between this row's node position and all others
delta = (pos[i] - pos).T
# distance between points
distance = np.sqrt((delta**2).sum(axis=0))
# enforce minimum distance of 0.01
distance = np.where(distance < 0.01, 0.01, distance)
# the adjacency matrix row
Ai = np.asarray(A.getrowview(i).toarray())
# displacement "force"
displacement[:, i] +=\
(delta * (k * k / distance**2 - Ai * distance / k)).sum(axis=1)
# update positions
length = np.sqrt((displacement**2).sum(axis=0))
length = np.where(length < 0.01, 0.1, length)
delta_pos = (displacement * t / length).T
pos += delta_pos
# cool temperature
t -= dt
err = np.linalg.norm(delta_pos)/nnodes
if err < threshold:
break
return pos
def _fruchterman_reingold(A, k=None, pos=None, fixed=None, iterations=50,
threshold=1e-4, dim=2, random_state=None):
# Position nodes in adjacency matrix A using Fruchterman-Reingold
# Entry point for NetworkX graph is fruchterman_reingold_layout()
try:
import numpy as np
except ImportError:
msg = "_fruchterman_reingold() requires numpy: http://scipy.org/ "
raise ImportError(msg)
try:
nnodes, _ = A.shape
except AttributeError:
msg = "fruchterman_reingold() takes an adjacency matrix as input"
raise nx.NetworkXError(msg)
# make sure we have an array instead of a matrix
A = np.asarray(A)
if pos is None:
# random initial positions
pos = np.asarray(random_state.rand(nnodes, dim), dtype=A.dtype)
else:
# make sure positions are of same type as matrix
pos = pos.astype(A.dtype)
# optimal distance between nodes
if k is None:
k = np.sqrt(1.0/nnodes)
# the initial "temperature" is about .1 of domain area (=1x1)
# this is the largest step allowed in the dynamics.
# We need to calculate this in case our fixed positions force our domain
# to be much bigger than 1x1
t = max(max(pos.T[0]) - min(pos.T[0]), max(pos.T[1]) - min(pos.T[1]))*0.1
# simple cooling scheme.
# linearly step down by dt on each iteration so last iteration is size dt.
dt = t/float(iterations+1)
delta = np.zeros((pos.shape[0], pos.shape[0], pos.shape[1]), dtype=A.dtype)
# the inscrutable (but fast) version
# this is still O(V^2)
# could use multilevel methods to speed this up significantly
for iteration in range(iterations):
# matrix of difference between points
delta = pos[:, np.newaxis, :] - pos[np.newaxis, :, :]
# distance between points
distance = np.linalg.norm(delta, axis=-1)
# enforce minimum distance of 0.01
np.clip(distance, 0.01, None, out=distance)
# displacement "force"
displacement = np.einsum('ijk,ij->ik',
delta,
(k * k / distance**2 - A * distance / k))
# update positions
length = np.linalg.norm(displacement, axis=-1)
length = np.where(length < 0.01, 0.1, length)
delta_pos = np.einsum('ij,i->ij', displacement, t / length)
if fixed is not None:
# don't change positions of fixed nodes
delta_pos[fixed] = 0.0
pos += delta_pos
# cool temperature
t -= dt
err = np.linalg.norm(delta_pos)/nnodes
if err < threshold:
break
return pos
def fruchterman_reingold_layout(G,
k=None,
pos=None,
fixed=None,
iterations=50,
threshold=1e-4,
weight='weight',
scale=1,
center=None,
dim=2,
random_state=None):
"""Position nodes using Fruchterman-Reingold force-directed algorithm.
Parameters
----------
G : NetworkX graph or list of nodes
A position will be assigned to every node in G.
k : float (default=None)
Optimal distance between nodes. If None the distance is set to
1/sqrt(n) where n is the number of nodes. Increase this value
to move nodes farther apart.
pos : dict or None optional (default=None)
Initial positions for nodes as a dictionary with node as keys
and values as a coordinate list or tuple. If None, then use
random initial positions.
fixed : list or None optional (default=None)
Nodes to keep fixed at initial position.
iterations : int optional (default=50)
Maximum number of iterations taken
threshold: float optional (default = 1e-4)
Threshold for relative error in node position changes.
The iteration stops if the error is below this threshold.
weight : string or None optional (default='weight')
The edge attribute that holds the numerical value used for
the edge weight. If None, then all edge weights are 1.
scale : number (default: 1)
Scale factor for positions. Not used unless `fixed is None`.
center : array-like or None
Coordinate pair around which to center the layout.
Not used unless `fixed is None`.
dim : int
Dimension of layout.
random_state : int, RandomState instance or None optional (default=None)
Set the random state for deterministic node layouts.
If int, `random_state` is the seed used by the random number generator,
if numpy.random.RandomState instance, `random_state` is the random
number generator,
if None, the random number generator is the RandomState instance used
by numpy.random.
Returns
-------
pos : dict
A dictionary of positions keyed by node
Examples
--------
>>> G = nx.path_graph(4)
>>> pos = nx.spring_layout(G)
# The same using longer but equivalent function name
>>> pos = nx.fruchterman_reingold_layout(G)
"""
import numpy as np
G, center = _process_params(G, center, dim)
if fixed is not None:
nfixed = dict(zip(G, range(len(G))))
fixed = np.asarray([nfixed[v] for v in fixed])
if pos is not None:
# Determine size of existing domain to adjust initial positions
dom_size = max(coord for pos_tup in pos.values() for coord in pos_tup)
if dom_size == 0:
dom_size = 1
shape = (len(G), dim)
pos_arr = random_state.rand(*shape) * dom_size + center
for i, n in enumerate(G):
if n in pos:
pos_arr[i] = np.asarray(pos[n])
else:
pos_arr = None
if len(G) == 0:
return {}
if len(G) == 1:
return {nx.utils.arbitrary_element(G.nodes()): center}
try:
# Sparse matrix
if len(G) < 500: # sparse solver for large graphs
raise ValueError
A = nx.to_scipy_sparse_matrix(G, weight=weight, dtype='f')
if k is None and fixed is not None:
# We must adjust k by domain size for layouts not near 1x1
nnodes, _ = A.shape
k = dom_size / np.sqrt(nnodes)
pos = _sparse_fruchterman_reingold(A, k, pos_arr, fixed,
iterations, threshold,
dim, random_state)
except:
A = nx.to_numpy_matrix(G, weight=weight)
if k is None and fixed is not None:
# We must adjust k by domain size for layouts not near 1x1
nnodes, _ = A.shape
k = dom_size / np.sqrt(nnodes)
pos = _fruchterman_reingold(A, k, pos_arr, fixed, iterations,
threshold, dim, random_state)
if fixed is None:
pos = rescale_layout(pos, scale=scale) + center
pos = dict(zip(G, pos))
return pos
