Source code for networkx.drawing.layout

"""
******
Layout
******

Node positioning algorithms for graph drawing.

For `random_layout()` the possible resulting shape
is a square of side [0, scale] (default: [0, 1])
Changing `center` shifts the layout by that amount.

For the other layout routines, the extent is
[center - scale, center + scale] (default: [-1, 1]).

Warning: Most layout routines have only been tested in 2-dimensions.

"""
import networkx as nx
from networkx.utils import random_state

__all__ = [
    "bipartite_layout",
    "circular_layout",
    "kamada_kawai_layout",
    "random_layout",
    "rescale_layout",
    "rescale_layout_dict",
    "shell_layout",
    "spring_layout",
    "spectral_layout",
    "planar_layout",
    "fruchterman_reingold_layout",
    "spiral_layout",
    "multipartite_layout",
]


def _process_params(G, center, dim):
    # Some boilerplate code.
    import numpy as np

    if not isinstance(G, nx.Graph):
        empty_graph = nx.Graph()
        empty_graph.add_nodes_from(G)
        G = empty_graph

    if center is None:
        center = np.zeros(dim)
    else:
        center = np.asarray(center)

    if len(center) != dim:
        msg = "length of center coordinates must match dimension of layout"
        raise ValueError(msg)

    return G, center


[docs]@random_state(3) def random_layout(G, center=None, dim=2, seed=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. seed : int, RandomState instance or None optional (default=None) Set the random state for deterministic node layouts. If int, `seed` is the seed used by the random number generator, if numpy.random.RandomState instance, `seed` 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) pos = seed.rand(len(G), dim) + center pos = pos.astype(np.float32) pos = dict(zip(G, pos)) return pos
[docs]def circular_layout(G, scale=1, center=None, dim=2): # dim=2 only """Position nodes on a circle. Parameters ---------- G : NetworkX graph or list of nodes A position will be assigned to every node in G. scale : number (default: 1) Scale factor for positions. center : array-like or None Coordinate pair around which to center the layout. dim : int Dimension of layout. If dim>2, the remaining dimensions are set to zero in the returned positions. If dim<2, a ValueError is raised. Returns ------- pos : dict A dictionary of positions keyed by node Raises ------ ValueError If dim < 2 Examples -------- >>> G = nx.path_graph(4) >>> pos = nx.circular_layout(G) Notes ----- This algorithm currently only works in two dimensions and does not try to minimize edge crossings. """ import numpy as np if dim < 2: raise ValueError("cannot handle dimensions < 2") G, center = _process_params(G, center, dim) paddims = max(0, (dim - 2)) if len(G) == 0: pos = {} elif len(G) == 1: pos = {nx.utils.arbitrary_element(G): center} else: # Discard the extra angle since it matches 0 radians. theta = np.linspace(0, 1, len(G) + 1)[:-1] * 2 * np.pi theta = theta.astype(np.float32) pos = np.column_stack( [np.cos(theta), np.sin(theta), np.zeros((len(G), paddims))] ) pos = rescale_layout(pos, scale=scale) + center pos = dict(zip(G, pos)) return pos
[docs]def shell_layout(G, nlist=None, rotate=None, scale=1, center=None, dim=2): """Position nodes in concentric circles. Parameters ---------- G : NetworkX graph or list of nodes A position will be assigned to every node in G. nlist : list of lists List of node lists for each shell. rotate : angle in radians (default=pi/len(nlist)) Angle by which to rotate the starting position of each shell relative to the starting position of the previous shell. To recreate behavior before v2.5 use rotate=0. scale : number (default: 1) Scale factor for positions. center : array-like or None Coordinate pair around which to center the layout. dim : int Dimension of layout, currently only dim=2 is supported. Other dimension values result in a ValueError. Returns ------- pos : dict A dictionary of positions keyed by node Raises ------ ValueError If dim != 2 Examples -------- >>> G = nx.path_graph(4) >>> shells = [[0], [1, 2, 3]] >>> pos = nx.shell_layout(G, shells) Notes ----- This algorithm currently only works in two dimensions and does not try to minimize edge crossings. """ import numpy as np if dim != 2: raise ValueError("can only handle 2 dimensions") G, center = _process_params(G, center, dim) if len(G) == 0: return {} if len(G) == 1: return {nx.utils.arbitrary_element(G): center} if nlist is None: # draw the whole graph in one shell nlist = [list(G)] radius_bump = scale / len(nlist) if len(nlist[0]) == 1: # single node at center radius = 0.0 else: # else start at r=1 radius = radius_bump if rotate is None: rotate = np.pi / len(nlist) first_theta = rotate npos = {} for nodes in nlist: # Discard the last angle (endpoint=False) since 2*pi matches 0 radians theta = ( np.linspace(0, 2 * np.pi, len(nodes), endpoint=False, dtype=np.float32) + first_theta ) pos = radius * np.column_stack([np.cos(theta), np.sin(theta)]) + center npos.update(zip(nodes, pos)) radius += radius_bump first_theta += rotate return npos
[docs]def bipartite_layout( G, nodes, align="vertical", scale=1, center=None, aspect_ratio=4 / 3 ): """Position nodes in two straight lines. Parameters ---------- G : NetworkX graph or list of nodes A position will be assigned to every node in G. nodes : list or container Nodes in one node set of the bipartite graph. This set will be placed on left or top. align : string (default='vertical') The alignment of nodes. Vertical or horizontal. scale : number (default: 1) Scale factor for positions. center : array-like or None Coordinate pair around which to center the layout. aspect_ratio : number (default=4/3): The ratio of the width to the height of the layout. Returns ------- pos : dict A dictionary of positions keyed by node. Examples -------- >>> G = nx.bipartite.gnmk_random_graph(3, 5, 10, seed=123) >>> top = nx.bipartite.sets(G)[0] >>> pos = nx.bipartite_layout(G, top) Notes ----- This algorithm currently only works in two dimensions and does not try to minimize edge crossings. """ import numpy as np if align not in ("vertical", "horizontal"): msg = "align must be either vertical or horizontal." raise ValueError(msg) G, center = _process_params(G, center=center, dim=2) if len(G) == 0: return {} height = 1 width = aspect_ratio * height offset = (width / 2, height / 2) top = set(nodes) bottom = set(G) - top nodes = list(top) + list(bottom) left_xs = np.repeat(0, len(top)) right_xs = np.repeat(width, len(bottom)) left_ys = np.linspace(0, height, len(top)) right_ys = np.linspace(0, height, len(bottom)) top_pos = np.column_stack([left_xs, left_ys]) - offset bottom_pos = np.column_stack([right_xs, right_ys]) - offset pos = np.concatenate([top_pos, bottom_pos]) pos = rescale_layout(pos, scale=scale) + center if align == "horizontal": pos = np.flip(pos, 1) pos = dict(zip(nodes, pos)) return pos
[docs]@random_state(10) def spring_layout( G, k=None, pos=None, fixed=None, iterations=50, threshold=1e-4, weight="weight", scale=1, center=None, dim=2, seed=None, ): """Position nodes using Fruchterman-Reingold force-directed algorithm. The algorithm simulates a force-directed representation of the network treating edges as springs holding nodes close, while treating nodes as repelling objects, sometimes called an anti-gravity force. Simulation continues until the positions are close to an equilibrium. There are some hard-coded values: minimal distance between nodes (0.01) and "temperature" of 0.1 to ensure nodes don't fly away. During the simulation, `k` helps determine the distance between nodes, though `scale` and `center` determine the size and place after rescaling occurs at the end of the simulation. Fixing some nodes doesn't allow them to move in the simulation. It also turns off the rescaling feature at the simulation's end. In addition, setting `scale` to `None` turns off rescaling. 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. Nodes not in ``G.nodes`` are ignored. ValueError raised if `fixed` specified and `pos` not. 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. Larger means a stronger attractive force. If None, then all edge weights are 1. scale : number or None (default: 1) Scale factor for positions. Not used unless `fixed is None`. If scale is None, no rescaling is performed. center : array-like or None Coordinate pair around which to center the layout. Not used unless `fixed is None`. dim : int Dimension of layout. seed : int, RandomState instance or None optional (default=None) Set the random state for deterministic node layouts. If int, `seed` is the seed used by the random number generator, if numpy.random.RandomState instance, `seed` 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: if pos is None: raise ValueError("nodes are fixed without positions given") for node in fixed: if node not in pos: raise ValueError("nodes are fixed without positions given") nfixed = {node: i for i, node in enumerate(G)} fixed = np.asarray([nfixed[node] for node in fixed if node in nfixed]) 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 pos_arr = seed.rand(len(G), dim) * dom_size + center for i, n in enumerate(G): if n in pos: pos_arr[i] = np.asarray(pos[n]) else: pos_arr = None dom_size = 1 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, seed ) except ValueError: A = nx.to_numpy_array(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, seed ) if fixed is None and scale is not None: pos = rescale_layout(pos, scale=scale) + center pos = dict(zip(G, pos)) return pos
fruchterman_reingold_layout = spring_layout @random_state(7) def _fruchterman_reingold( A, k=None, pos=None, fixed=None, iterations=50, threshold=1e-4, dim=2, seed=None ): # Position nodes in adjacency matrix A using Fruchterman-Reingold # Entry point for NetworkX graph is fruchterman_reingold_layout() import numpy as np try: nnodes, _ = A.shape except AttributeError as e: msg = "fruchterman_reingold() takes an adjacency matrix as input" raise nx.NetworkXError(msg) from e if pos is None: # random initial positions pos = np.asarray(seed.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 @random_state(7) def _sparse_fruchterman_reingold( A, k=None, pos=None, fixed=None, iterations=50, threshold=1e-4, dim=2, seed=None ): # Position nodes in adjacency matrix A using Fruchterman-Reingold # Entry point for NetworkX graph is fruchterman_reingold_layout() # Sparse version import numpy as np import scipy as sp import scipy.sparse # call as sp.sparse try: nnodes, _ = A.shape except AttributeError as e: msg = "fruchterman_reingold() takes an adjacency matrix as input" raise nx.NetworkXError(msg) from e # make sure we have a LIst of Lists representation try: A = A.tolil() except AttributeError: A = (sp.sparse.coo_matrix(A)).tolil() if pos is None: # random initial positions pos = np.asarray(seed.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
[docs]def kamada_kawai_layout( G, dist=None, pos=None, weight="weight", scale=1, center=None, dim=2 ): """Position nodes using Kamada-Kawai path-length cost-function. Parameters ---------- G : NetworkX graph or list of nodes A position will be assigned to every node in G. dist : dict (default=None) A two-level dictionary of optimal distances between nodes, indexed by source and destination node. If None, the distance is computed using shortest_path_length(). 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 circular_layout() for dim >= 2 and a linear layout for dim == 1. 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. center : array-like or None Coordinate pair around which to center the layout. dim : int Dimension of layout. Returns ------- pos : dict A dictionary of positions keyed by node Examples -------- >>> G = nx.path_graph(4) >>> pos = nx.kamada_kawai_layout(G) """ import numpy as np G, center = _process_params(G, center, dim) nNodes = len(G) if nNodes == 0: return {} if dist is None: dist = dict(nx.shortest_path_length(G, weight=weight)) dist_mtx = 1e6 * np.ones((nNodes, nNodes)) for row, nr in enumerate(G): if nr not in dist: continue rdist = dist[nr] for col, nc in enumerate(G): if nc not in rdist: continue dist_mtx[row][col] = rdist[nc] if pos is None: if dim >= 3: pos = random_layout(G, dim=dim) elif dim == 2: pos = circular_layout(G, dim=dim) else: pos = {n: pt for n, pt in zip(G, np.linspace(0, 1, len(G)))} pos_arr = np.array([pos[n] for n in G]) pos = _kamada_kawai_solve(dist_mtx, pos_arr, dim) pos = rescale_layout(pos, scale=scale) + center return dict(zip(G, pos))
def _kamada_kawai_solve(dist_mtx, pos_arr, dim): # Anneal node locations based on the Kamada-Kawai cost-function, # using the supplied matrix of preferred inter-node distances, # and starting locations. import numpy as np import scipy as sp import scipy.optimize # call as sp.optimize meanwt = 1e-3 costargs = (np, 1 / (dist_mtx + np.eye(dist_mtx.shape[0]) * 1e-3), meanwt, dim) optresult = sp.optimize.minimize( _kamada_kawai_costfn, pos_arr.ravel(), method="L-BFGS-B", args=costargs, jac=True, ) return optresult.x.reshape((-1, dim)) def _kamada_kawai_costfn(pos_vec, np, invdist, meanweight, dim): # Cost-function and gradient for Kamada-Kawai layout algorithm nNodes = invdist.shape[0] pos_arr = pos_vec.reshape((nNodes, dim)) delta = pos_arr[:, np.newaxis, :] - pos_arr[np.newaxis, :, :] nodesep = np.linalg.norm(delta, axis=-1) direction = np.einsum("ijk,ij->ijk", delta, 1 / (nodesep + np.eye(nNodes) * 1e-3)) offset = nodesep * invdist - 1.0 offset[np.diag_indices(nNodes)] = 0 cost = 0.5 * np.sum(offset ** 2) grad = np.einsum("ij,ij,ijk->ik", invdist, offset, direction) - np.einsum( "ij,ij,ijk->jk", invdist, offset, direction ) # Additional parabolic term to encourage mean position to be near origin: sumpos = np.sum(pos_arr, axis=0) cost += 0.5 * meanweight * np.sum(sumpos ** 2) grad += meanweight * sumpos return (cost, grad.ravel())
[docs]def spectral_layout(G, weight="weight", scale=1, center=None, dim=2): """Position nodes using the eigenvectors of the graph Laplacian. Using the unnormalized Laplacian, the layout shows possible clusters of nodes which are an approximation of the ratio cut. If dim is the number of dimensions then the positions are the entries of the dim eigenvectors corresponding to the ascending eigenvalues starting from the second one. Parameters ---------- G : NetworkX graph or list of nodes A position will be assigned to every node in G. 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. center : array-like or None Coordinate pair around which to center the layout. dim : int Dimension of layout. Returns ------- pos : dict A dictionary of positions keyed by node Examples -------- >>> G = nx.path_graph(4) >>> pos = nx.spectral_layout(G) Notes ----- Directed graphs will be considered as undirected graphs when positioning the nodes. For larger graphs (>500 nodes) this will use the SciPy sparse eigenvalue solver (ARPACK). """ # handle some special cases that break the eigensolvers import numpy as np G, center = _process_params(G, center, dim) if len(G) <= 2: if len(G) == 0: pos = np.array([]) elif len(G) == 1: pos = np.array([center]) else: pos = np.array([np.zeros(dim), np.array(center) * 2.0]) return dict(zip(G, pos)) try: # Sparse matrix if len(G) < 500: # dense solver is faster for small graphs raise ValueError A = nx.to_scipy_sparse_matrix(G, weight=weight, dtype="d") # Symmetrize directed graphs if G.is_directed(): A = A + np.transpose(A) pos = _sparse_spectral(A, dim) except (ImportError, ValueError): # Dense matrix A = nx.to_numpy_array(G, weight=weight) # Symmetrize directed graphs if G.is_directed(): A += A.T pos = _spectral(A, dim) pos = rescale_layout(pos, scale=scale) + center pos = dict(zip(G, pos)) return pos
def _spectral(A, dim=2): # Input adjacency matrix A # Uses dense eigenvalue solver from numpy import numpy as np try: nnodes, _ = A.shape except AttributeError as e: msg = "spectral() takes an adjacency matrix as input" raise nx.NetworkXError(msg) from e # form Laplacian matrix where D is diagonal of degrees D = np.identity(nnodes, dtype=A.dtype) * np.sum(A, axis=1) L = D - A eigenvalues, eigenvectors = np.linalg.eig(L) # sort and keep smallest nonzero index = np.argsort(eigenvalues)[1 : dim + 1] # 0 index is zero eigenvalue return np.real(eigenvectors[:, index]) def _sparse_spectral(A, dim=2): # Input adjacency matrix A # Uses sparse eigenvalue solver from scipy # Could use multilevel methods here, see Koren "On spectral graph drawing" import numpy as np import scipy as sp import scipy.sparse # call as sp.sparse import scipy.sparse.linalg # call as sp.sparse.linalg try: nnodes, _ = A.shape except AttributeError as e: msg = "sparse_spectral() takes an adjacency matrix as input" raise nx.NetworkXError(msg) from e # form Laplacian matrix data = np.asarray(A.sum(axis=1).T) D = sp.sparse.spdiags(data, 0, nnodes, nnodes) L = D - A k = dim + 1 # number of Lanczos vectors for ARPACK solver.What is the right scaling? ncv = max(2 * k + 1, int(np.sqrt(nnodes))) # return smallest k eigenvalues and eigenvectors eigenvalues, eigenvectors = sp.sparse.linalg.eigen.eigsh(L, k, which="SM", ncv=ncv) index = np.argsort(eigenvalues)[1:k] # 0 index is zero eigenvalue return np.real(eigenvectors[:, index])
[docs]def planar_layout(G, scale=1, center=None, dim=2): """Position nodes without edge intersections. Parameters ---------- G : NetworkX graph or list of nodes A position will be assigned to every node in G. If G is of type nx.PlanarEmbedding, the positions are selected accordingly. scale : number (default: 1) Scale factor for positions. center : array-like or None Coordinate pair around which to center the layout. dim : int Dimension of layout. Returns ------- pos : dict A dictionary of positions keyed by node Raises ------ NetworkXException If G is not planar Examples -------- >>> G = nx.path_graph(4) >>> pos = nx.planar_layout(G) """ import numpy as np if dim != 2: raise ValueError("can only handle 2 dimensions") G, center = _process_params(G, center, dim) if len(G) == 0: return {} if isinstance(G, nx.PlanarEmbedding): embedding = G else: is_planar, embedding = nx.check_planarity(G) if not is_planar: raise nx.NetworkXException("G is not planar.") pos = nx.combinatorial_embedding_to_pos(embedding) node_list = list(embedding) pos = np.row_stack([pos[x] for x in node_list]) pos = pos.astype(np.float64) pos = rescale_layout(pos, scale=scale) + center return dict(zip(node_list, pos))
[docs]def spiral_layout(G, scale=1, center=None, dim=2, resolution=0.35, equidistant=False): """Position nodes in a spiral layout. Parameters ---------- G : NetworkX graph or list of nodes A position will be assigned to every node in G. scale : number (default: 1) Scale factor for positions. center : array-like or None Coordinate pair around which to center the layout. dim : int Dimension of layout, currently only dim=2 is supported. Other dimension values result in a ValueError. resolution : float The compactness of the spiral layout returned. Lower values result in more compressed spiral layouts. equidistant : bool If True, nodes will be plotted equidistant from each other. Returns ------- pos : dict A dictionary of positions keyed by node Raises ------ ValueError If dim != 2 Examples -------- >>> G = nx.path_graph(4) >>> pos = nx.spiral_layout(G) Notes ----- This algorithm currently only works in two dimensions. """ import numpy as np if dim != 2: raise ValueError("can only handle 2 dimensions") G, center = _process_params(G, center, dim) if len(G) == 0: return {} if len(G) == 1: return {nx.utils.arbitrary_element(G): center} pos = [] if equidistant: chord = 1 step = 0.5 theta = resolution for _ in range(len(G)): r = step * theta theta += chord / r pos.append([np.cos(theta) * r, np.sin(theta) * r]) else: # set the starting angle and step step = 1 angle = 0.0 dist = 0.0 # set the radius for the spiral to the number of nodes in the graph radius = len(G) while dist * np.hypot(np.cos(angle), np.sin(angle)) < radius: pos.append([dist * np.cos(angle), dist * np.sin(angle)]) dist += step angle += resolution pos = rescale_layout(np.array(pos), scale=scale) + center pos = dict(zip(G, pos)) return pos
[docs]def multipartite_layout(G, subset_key="subset", align="vertical", scale=1, center=None): """Position nodes in layers of straight lines. Parameters ---------- G : NetworkX graph or list of nodes A position will be assigned to every node in G. subset_key : string (default='subset') Key of node data to be used as layer subset. align : string (default='vertical') The alignment of nodes. Vertical or horizontal. scale : number (default: 1) Scale factor for positions. center : array-like or None Coordinate pair around which to center the layout. Returns ------- pos : dict A dictionary of positions keyed by node. Examples -------- >>> G = nx.complete_multipartite_graph(28, 16, 10) >>> pos = nx.multipartite_layout(G) Notes ----- This algorithm currently only works in two dimensions and does not try to minimize edge crossings. Network does not need to be a complete multipartite graph. As long as nodes have subset_key data, they will be placed in the corresponding layers. """ import numpy as np if align not in ("vertical", "horizontal"): msg = "align must be either vertical or horizontal." raise ValueError(msg) G, center = _process_params(G, center=center, dim=2) if len(G) == 0: return {} layers = {} for v, data in G.nodes(data=True): try: layer = data[subset_key] except KeyError: msg = "all nodes must have subset_key (default='subset') as data" raise ValueError(msg) layers[layer] = [v] + layers.get(layer, []) pos = None nodes = [] width = len(layers) for i, layer in layers.items(): height = len(layer) xs = np.repeat(i, height) ys = np.arange(0, height, dtype=float) offset = ((width - 1) / 2, (height - 1) / 2) layer_pos = np.column_stack([xs, ys]) - offset if pos is None: pos = layer_pos else: pos = np.concatenate([pos, layer_pos]) nodes.extend(layer) pos = rescale_layout(pos, scale=scale) + center if align == "horizontal": pos = np.flip(pos, 1) pos = dict(zip(nodes, pos)) return pos
[docs]def rescale_layout(pos, scale=1): """Returns scaled position array to (-scale, scale) in all axes. The function acts on NumPy arrays which hold position information. Each position is one row of the array. The dimension of the space equals the number of columns. Each coordinate in one column. To rescale, the mean (center) is subtracted from each axis separately. Then all values are scaled so that the largest magnitude value from all axes equals `scale` (thus, the aspect ratio is preserved). The resulting NumPy Array is returned (order of rows unchanged). Parameters ---------- pos : numpy array positions to be scaled. Each row is a position. scale : number (default: 1) The size of the resulting extent in all directions. Returns ------- pos : numpy array scaled positions. Each row is a position. See Also -------- rescale_layout_dict """ # Find max length over all dimensions lim = 0 # max coordinate for all axes for i in range(pos.shape[1]): pos[:, i] -= pos[:, i].mean() lim = max(abs(pos[:, i]).max(), lim) # rescale to (-scale, scale) in all directions, preserves aspect if lim > 0: for i in range(pos.shape[1]): pos[:, i] *= scale / lim return pos
[docs]def rescale_layout_dict(pos, scale=1): """Return a dictionary of scaled positions keyed by node Parameters ---------- pos : A dictionary of positions keyed by node scale : number (default: 1) The size of the resulting extent in all directions. Returns ------- pos : A dictionary of positions keyed by node Examples -------- >>> pos = {0: (0, 0), 1: (1, 1), 2: (0.5, 0.5)} >>> nx.rescale_layout_dict(pos) {0: (-1.0, -1.0), 1: (1.0, 1.0), 2: (0.0, 0.0)} >>> pos = {0: (0, 0), 1: (-1, 1), 2: (-0.5, 0.5)} >>> nx.rescale_layout_dict(pos, scale=2) {0: (2.0, -2.0), 1: (-2.0, 2.0), 2: (0.0, 0.0)} See Also -------- rescale_layout """ import numpy as np if not pos: # empty_graph return {} pos_v = np.array(list(pos.values())) pos_v = rescale_layout(pos_v, scale=scale) return {k: tuple(v) for k, v in zip(pos.keys(), pos_v)}