Merge pull request #1760 from dschult/fix-layoutv1.10.1

Fix layout.py and revert changes to default scales.

3 files changed, 237 insertions, 164 deletions

diff --git a/doc/source/reference/drawing.rst b/doc/source/reference/drawing.rst
index b5a76b7b..41f00aad 100644
--- a/doc/source/reference/drawing.rst
+++ b/doc/source/reference/drawing.rst
@@ -78,6 +78,7 @@ Graph Layout
    :toctree: generated/
 
    circular_layout
+   fruchterman_reingold_layout
    random_layout
    shell_layout
    spring_layout
diff --git a/networkx/drawing/layout.py b/networkx/drawing/layout.py
index 5d9cc991..3b93bbde 100644
--- a/networkx/drawing/layout.py
+++ b/networkx/drawing/layout.py
@@ -4,6 +4,11 @@ Layout
 ******
 
 Node positioning algorithms for graph drawing.
+
+The default scales and centering for these layouts are 
+typically squares with side [0, 1] or [0, scale].
+The two circular layout routines (circular_layout and
+shell_layout) have size [-1, 1] or [-scale, scale].
 """
 #    Copyright (C) 2004-2015 by
 #    Aric Hagberg <hagberg@lanl.gov>
@@ -13,7 +18,8 @@ Node positioning algorithms for graph drawing.
 #    BSD license.
 import collections
 import networkx as nx
-__author__ = """Aric Hagberg (hagberg@lanl.gov)\nDan Schult(dschult@colgate.edu)"""
+__author__ = """\n""".join(['Aric Hagberg <aric.hagberg@gmail.com>',
+                           'Dan Schult(dschult@colgate.edu)'])
 __all__ = ['circular_layout',
            'random_layout',
            'shell_layout',
@@ -21,32 +27,13 @@ __all__ = ['circular_layout',
            'spectral_layout',
            'fruchterman_reingold_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
 
-
-def random_layout(G, dim=2, center=None):
-    """Position nodes uniformly at random in the unit square.
+def random_layout(G, dim=2, scale=1., center=None):
+    """Position nodes uniformly at random.
 
     For every node, a position is generated by choosing each of dim
-    coordinates uniformly at random on the interval [0.0, 1.0).
+    coordinates uniformly at random on the default interval [0.0, 1.0),
+    or on an interval of length `scale` centered at `center`.
 
     NumPy (http://scipy.org) is required for this function.
 
@@ -58,8 +45,11 @@ def random_layout(G, dim=2, center=None):
     dim : int
        Dimension of layout.
 
-    center : array-like or None
-       Coordinate pair around which to center the layout.
+    scale : float (default 1)
+        Scale factor for positions
+
+    center : array-like (default scale*0.5 in each dim)
+       Coordinate around which to center the layout.
 
     Returns
     -------
@@ -70,21 +60,17 @@ def random_layout(G, dim=2, center=None):
     --------
     >>> 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 = np.random.random(shape) + center
-    pos = pos.astype(np.float32)
-    pos = dict(zip(G, pos))
-
-    return pos
+    pos = np.random.random(shape) * scale
+    if center is not None:
+        pos += np.asarray(center) - 0.5 * scale
+    return dict(zip(G, pos))
 
 
-def circular_layout(G, dim=2, scale=1, center=None):
-    # dim=2 only
+def circular_layout(G, dim=2, scale=1., center=None):
     """Position nodes on a circle.
 
     Parameters
@@ -94,11 +80,11 @@ def circular_layout(G, dim=2, scale=1, center=None):
     dim : int
        Dimension of layout, currently only dim=2 is supported
 
-    scale : float
-        Scale factor for positions
+    scale : float (default 1)
+        Scale factor for positions, i.e. radius of circle.
 
-    center : array-like or None
-       Coordinate pair around which to center the layout.
+    center : array-like (default origin)
+       Coordinate around which to center the layout.
 
     Returns
     -------
@@ -118,23 +104,18 @@ def circular_layout(G, dim=2, scale=1, center=None):
     """
     import numpy as np
 
-    G, center = process_params(G, center, dim)
-
     if len(G) == 0:
-        pos = {}
-    elif len(G) == 1:
-        pos = {G.nodes()[0]: 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)])
-        pos = _rescale_layout(pos, scale=scale) + center
-        pos = dict(zip(G, pos))
+        return {}
 
-    return pos
+    twopi = 2.0*np.pi
+    theta = np.arange(0, twopi, twopi/len(G))
+    pos = np.column_stack([np.cos(theta), np.sin(theta)]) * scale
+    if center is not None:
+        pos += np.asarray(center)
 
-def shell_layout(G, nlist=None, dim=2, scale=1, center=None):
+    return dict(zip(G, pos))
+
+def shell_layout(G, nlist=None, dim=2, scale=1., center=None):
     """Position nodes in concentric circles.
 
     Parameters
@@ -147,11 +128,11 @@ def shell_layout(G, nlist=None, dim=2, scale=1, center=None):
     dim : int
        Dimension of layout, currently only dim=2 is supported
 
-    scale : float
-        Scale factor for positions
+    scale : float (default 1)
+        Scale factor for positions, i.e.radius of largest shell
 
-    center : array-like or None
-       Coordinate pair around which to center the layout.
+    center : array-like (default origin)
+       Coordinate around which to center the layout.
 
     Returns
     -------
@@ -172,39 +153,42 @@ def shell_layout(G, nlist=None, dim=2, scale=1, center=None):
     """
     import numpy as np
 
-    G, center = process_params(G, center, dim)
-
     if len(G) == 0:
         return {}
-    elif len(G) == 1:
-        return {G.nodes()[0]: center}
-
 
     if nlist is None:
         # draw the whole graph in one shell
-        nlist = [list(G.nodes())]
+        nlist = [list(G)]
 
+    numb_shells = len(nlist)
     if len(nlist[0]) == 1:
         # single node at center
         radius = 0.0
+        numb_shells -= 1
     else:
         # else start at r=1
         radius = 1.0
+    # distance between shells
+    gap = (scale / numb_shells) if numb_shells else scale
+    radius *= gap
 
     npos={}
+    twopi = 2.0*np.pi
     for nodes in nlist:
-        # Discard the extra angle since it matches 0 radians.
-        theta = np.linspace(0, 1, len(nodes) + 1)[:-1] * 2 * np.pi
-        theta = theta.astype(np.float32)
-        pos = np.column_stack([np.cos(theta), np.sin(theta)])
-        pos = _rescale_layout(pos, scale=scale * radius / len(nlist)) + center
+        theta = np.arange(0, twopi, twopi/len(nodes))
+        pos = np.column_stack([np.cos(theta), np.sin(theta)]) * radius
         npos.update(zip(nodes, pos))
-        radius += 1.0
+        radius += gap
+
+    if center is not None:
+        center = np.asarray(center)
+        for n,p in npos.items():
+            npos[n] = p + center
 
     return npos
 
 
-def fruchterman_reingold_layout(G,dim=2,k=None,
+def fruchterman_reingold_layout(G, dim=2, k=None,
                                 pos=None,
                                 fixed=None,
                                 iterations=50,
@@ -215,7 +199,7 @@ def fruchterman_reingold_layout(G,dim=2,k=None,
 
     Parameters
     ----------
-    G : NetworkX graph or list of nodes
+    G : NetworkX graph
 
     dim : int
        Dimension of layout
@@ -225,7 +209,6 @@ def fruchterman_reingold_layout(G,dim=2,k=None,
        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 list or tuple.  If None, then use random initial
@@ -233,21 +216,21 @@ def fruchterman_reingold_layout(G,dim=2,k=None,
 
     fixed : list or None  optional (default=None)
       Nodes to keep fixed at initial position.
+      If any nodes are fixed, the scale and center features are not used.
 
     iterations : int  optional (default=50)
        Number of iterations of spring-force relaxation
 
     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.
+        the effective spring constant. If None, edge weights are 1.
 
     scale : float (default=1.0)
         Scale factor for positions. The nodes are positioned
-        in a box of size [0,scale] x [0,scale].
-
-    center : array-like or None
-       Coordinate pair around which to center the layout.
+        in a box of size `scale` in each dim centered at `center`.
 
+    center : array-like (default scale/2 in each dim)
+       Coordinate around which to center the layout.
 
     Returns
     -------
@@ -259,66 +242,62 @@ def fruchterman_reingold_layout(G,dim=2,k=None,
     >>> G=nx.path_graph(4)
     >>> pos=nx.spring_layout(G)
 
-    # The same using longer function name
+    # this function has two names:
+    # spring_layout and fruchterman_reingold_layout
     >>> pos=nx.fruchterman_reingold_layout(G)
     """
     import numpy as np
 
-    G, center = process_params(G, center, dim)
+    if len(G) == 0:
+        return {}
 
     if fixed is not None:
         nfixed = dict(zip(G, range(len(G))))
         fixed = np.asarray([nfixed[v] for v in fixed])
 
+        if pos is None:
+            msg = "Keyword pos must be specified if any nodes are fixed"
+            raise ValueError(msg)
+
     if pos is not None:
         # Determine size of existing domain to adjust initial positions
-        dom_size = max(flatten(pos.values()))
+        pos_coords = np.array(list(pos.values()))
+        min_coords = pos_coords.min(0)
+        domain_size = pos_coords.max(0) - min_coords
         shape = (len(G), dim)
-        pos_arr = np.random.random(shape) * dom_size + center
+        pos_arr = np.random.random(shape) * domain_size + min_coords
         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 {G.nodes()[0]: center}
-
+    if k is None and fixed is not None:
+        # Adjust k for domains larger than 1x1
+        k=domain_size.max()/np.sqrt(len(G))
     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 that are not near 1x1
-           nnodes,_ = A.shape
-           k = dom_size / np.sqrt(nnodes)
-        pos = _sparse_fruchterman_reingold(A, dim, k, pos_arr, fixed, iterations)
+        A = nx.to_scipy_sparse_matrix(G, weight=weight, dtype='f')
+        pos = _sparse_fruchterman_reingold(A,dim,k,pos_arr,fixed,iterations)
     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 that are not near 1x1
-           nnodes,_ = A.shape
-           k = dom_size / np.sqrt(nnodes)
+        A = nx.to_numpy_matrix(G, weight=weight)
         pos = _fruchterman_reingold(A, dim, k, pos_arr, fixed, iterations)
+
     if fixed is None:
-        pos = _rescale_layout(pos, scale=scale) + center
-    pos = dict(zip(G,pos))
-    return pos
+        pos = _rescale_layout(pos, scale)
+        if center is not None:
+            pos += np.asarray(center) - 0.5 * scale
+
+    return dict(zip(G,pos))
 
 spring_layout=fruchterman_reingold_layout
 
-def _fruchterman_reingold(A, dim=2, k=None, pos=None, fixed=None,
-                          iterations=50):
+def _fruchterman_reingold(A,dim=2,k=None,pos=None,fixed=None,iterations=50):
     # 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:
-        raise ImportError("_fruchterman_reingold() requires numpy: http://scipy.org/ ")
-
+    import numpy as np
     try:
         nnodes,_=A.shape
     except AttributeError:
@@ -327,7 +306,7 @@ def _fruchterman_reingold(A, dim=2, k=None, pos=None, fixed=None,
 
     A=np.asarray(A) # make sure we have an array instead of a matrix
 
-    if pos==None:
+    if pos is None:
         # random initial positions
         pos=np.asarray(np.random.random((nnodes,dim)),dtype=A.dtype)
     else:
@@ -339,8 +318,7 @@ def _fruchterman_reingold(A, dim=2, k=None, pos=None, fixed=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
+    # Calculate domain in case our fixed positions are 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.
@@ -363,7 +341,7 @@ def _fruchterman_reingold(A, dim=2, k=None, pos=None, fixed=None,
                                   .sum(axis=1)
         # update positions
         length=np.sqrt((displacement**2).sum(axis=1))
-        length=np.where(length<0.01,0.1,length)
+        length=np.where(length<0.01,0.01,length)
         delta_pos=np.transpose(np.transpose(displacement)*t/length)
         if fixed is not None:
             # don't change positions of fixed nodes
@@ -371,6 +349,8 @@ def _fruchterman_reingold(A, dim=2, k=None, pos=None, fixed=None,
         pos+=delta_pos
         # cool temperature
         t-=dt
+        if fixed is None:
+            pos = _rescale_layout(pos)
     return pos
 
 
@@ -379,10 +359,7 @@ def _sparse_fruchterman_reingold(A, dim=2, k=None, pos=None, fixed=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:
-        raise ImportError("_sparse_fruchterman_reingold() requires numpy: http://scipy.org/ ")
+    import numpy as np
     try:
         nnodes,_=A.shape
     except AttributeError:
@@ -398,7 +375,7 @@ def _sparse_fruchterman_reingold(A, dim=2, k=None, pos=None, fixed=None,
     except:
         A=(coo_matrix(A)).tolil()
 
-    if pos==None:
+    if pos is None:
         # random initial positions
         pos=np.asarray(np.random.random((nnodes,dim)),dtype=A.dtype)
     else:
@@ -406,7 +383,7 @@ def _sparse_fruchterman_reingold(A, dim=2, k=None, pos=None, fixed=None,
         pos=pos.astype(A.dtype)
 
     # no fixed nodes
-    if fixed==None:
+    if fixed is None:
         fixed=[]
 
     # optimal distance between nodes
@@ -414,7 +391,8 @@ def _sparse_fruchterman_reingold(A, dim=2, k=None, pos=None, fixed=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
+    # Calculate domain in case our fixed positions are 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)
@@ -439,14 +417,16 @@ def _sparse_fruchterman_reingold(A, dim=2, k=None, pos=None, fixed=None,
                 (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)
+        length=np.where(length<0.01,0.01,length)
         pos+=(displacement*t/length).T
         # cool temperature
         t-=dt
+        if fixed is None:
+            pos = _rescale_layout(pos)
     return pos
 
 
-def spectral_layout(G, dim=2, weight='weight', scale=1, center=None):
+def spectral_layout(G, dim=2, weight='weight', scale=1., center=None):
     """Position nodes using the eigenvectors of the graph Laplacian.
 
     Parameters
@@ -460,11 +440,12 @@ def spectral_layout(G, dim=2, weight='weight', scale=1, center=None):
         The edge attribute that holds the numerical value used for
         the edge weight.  If None, then all edge weights are 1.
 
-    scale : float
-        Scale factor for positions
+    scale : float optional (default 1)
+        Scale factor for positions, i.e. nodes placed in a box with
+        side [0, scale] or centered on `center` if provided.
 
-    center : array-like or None
-       Coordinate pair around which to center the layout.
+    center : array-like (default scale/2 in each dim)
+       Coordinate around which to center the layout.
 
     Returns
     -------
@@ -487,15 +468,18 @@ def spectral_layout(G, dim=2, weight='weight', scale=1, center=None):
     # 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([])
+            return {}
         elif len(G) == 1:
-            pos = np.array([center])
-        else:
-            pos = np.array([np.zeros(dim), np.array(center)*2.0])
+            if center is not None:
+                pos = np.asarray(center)
+            else:
+                pos = np.ones((1,dim)) * scale * 0.5
+        else: #len(G) == 2
+            pos = np.array([np.zeros(dim), np.ones(dim) * scale])
+            if center is not None:
+                pos += np.asarray(center) - scale * 0.5
         return dict(zip(G,pos))
     try:
         # Sparse matrix
@@ -514,9 +498,11 @@ def spectral_layout(G, dim=2, weight='weight', scale=1, center=None):
             A = A + np.transpose(A)
         pos = _spectral(A, dim)
 
-    pos = _rescale_layout(pos, scale) + center
-    pos = dict(zip(G,pos))
-    return pos
+    pos = _rescale_layout(pos, scale)
+    if center is not None:
+        pos += np.asarray(center) - 0.5 * scale
+
+    return dict(zip(G,pos))
 
 
 def _spectral(A, dim=2):
@@ -578,20 +564,19 @@ def _sparse_spectral(A,dim=2):
     return np.real(eigenvectors[:,index])
 
 
-def _rescale_layout(pos,scale=1):
-    # rescale to (-scale,scale) in all axes
+def _rescale_layout(pos, scale=1.):
+    # rescale to [0, scale) in each axis
 
-    # shift origin to (0,0)
-    lim=0 # max coordinate for all axes
-    for i in range(pos.shape[1]):
-        pos[:,i]-=pos[:,i].mean()
-        lim=max(pos[:,i].max(),lim)
-    # rescale to (-scale,scale) in all directions, preserves aspect
+    # Find max length over all dimensions
+    maxlim=0 
     for i in range(pos.shape[1]):
-        pos[:,i]*=scale/lim
+        pos[:,i] -= pos[:,i].min() # shift min to zero
+        maxlim = max(maxlim, pos[:,i].max())
+    if maxlim > 0:
+        for i in range(pos.shape[1]):
+            pos[:,i] *= scale / maxlim
     return pos
 
-
 # fixture for nose tests
 def setup_module(module):
     from nose import SkipTest
@@ -603,17 +588,3 @@ def setup_module(module):
         import scipy
     except:
         raise SkipTest("SciPy not available")
-
-def flatten(l):
-    try:
-        bs = basestring
-    except NameError:
-        # Py3k
-        bs = str
-    for el in l:
-        if isinstance(el, collections.Iterable) and not isinstance(el, bs):
-            for sub in flatten(el):
-                yield sub
-        else:
-            yield el
-
diff --git a/networkx/drawing/tests/test_layout.py b/networkx/drawing/tests/test_layout.py
index bcd6d236..8366d252 100644
--- a/networkx/drawing/tests/test_layout.py
+++ b/networkx/drawing/tests/test_layout.py
@@ -32,14 +32,115 @@ class TestLayout(object):
         vpos=nx.shell_layout(G)
 
     def test_smoke_string(self):
-        G=self.Gs
-        vpos=nx.random_layout(G)
-        vpos=nx.circular_layout(G)
-        vpos=nx.spring_layout(G)
-        vpos=nx.fruchterman_reingold_layout(G)
-        vpos=nx.spectral_layout(G)
-        vpos=nx.shell_layout(G)
+        G = self.Gs
+        vpos = nx.random_layout(G)
+        vpos = nx.circular_layout(G)
+        vpos = nx.spring_layout(G)
+        vpos = nx.fruchterman_reingold_layout(G)
+        vpos = nx.spectral_layout(G)
+        vpos = nx.shell_layout(G)
+
+    def test_empty_graph(self):
+        G=nx.Graph()
+        vpos = nx.random_layout(G)
+        vpos = nx.circular_layout(G)
+        vpos = nx.spring_layout(G)
+        vpos = nx.fruchterman_reingold_layout(G)
+        vpos = nx.shell_layout(G)
+        vpos = nx.spectral_layout(G)
+        # center arg
+        vpos = nx.random_layout(G, scale=2, center=(4,5))
+        vpos = nx.circular_layout(G, scale=2, center=(4,5))
+        vpos = nx.spring_layout(G, scale=2, center=(4,5))
+        vpos = nx.shell_layout(G, scale=2, center=(4,5))
+        vpos = nx.spectral_layout(G, scale=2, center=(4,5))
+
+    def test_single_node(self):
+        G = nx.Graph()
+        G.add_node(0)
+        vpos = nx.random_layout(G)
+        vpos = nx.circular_layout(G)
+        vpos = nx.spring_layout(G)
+        vpos = nx.fruchterman_reingold_layout(G)
+        vpos = nx.shell_layout(G)
+        vpos = nx.spectral_layout(G)
+        # center arg
+        vpos = nx.random_layout(G, scale=2, center=(4,5))
+        vpos = nx.circular_layout(G, scale=2, center=(4,5))
+        vpos = nx.spring_layout(G, scale=2, center=(4,5))
+        vpos = nx.shell_layout(G, scale=2, center=(4,5))
+        vpos = nx.spectral_layout(G, scale=2, center=(4,5))
+
+    def check_scale_and_center(self, pos, scale, center):
+        center = numpy.array(center)
+        low = center - 0.5 * scale
+        hi = center + 0.5 * scale
+        vpos = numpy.array(list(pos.values()))
+        length = vpos.max(0) - vpos.min(0)
+        assert (length <= scale).all()
+        assert (vpos >= low).all()
+        assert (vpos <= hi).all()
+
+    def test_scale_and_center_arg(self):
+        G = nx.complete_graph(9)
+        G.add_node(9)
+        vpos = nx.random_layout(G, scale=2, center=(4,5))
+        self.check_scale_and_center(vpos, scale=2, center=(4,5))
+        vpos = nx.spring_layout(G, scale=2, center=(4,5))
+        self.check_scale_and_center(vpos, scale=2, center=(4,5))
+        vpos = nx.spectral_layout(G, scale=2, center=(4,5))
+        self.check_scale_and_center(vpos, scale=2, center=(4,5))
+        # circular can have twice as big length
+        vpos = nx.circular_layout(G, scale=2, center=(4,5))
+        self.check_scale_and_center(vpos, scale=2*2, center=(4,5))
+        vpos = nx.shell_layout(G, scale=2, center=(4,5))
+        self.check_scale_and_center(vpos, scale=2*2, center=(4,5))
+
+        # check default center and scale
+        vpos = nx.random_layout(G)
+        self.check_scale_and_center(vpos, scale=1, center=(0.5,0.5))
+        vpos = nx.spring_layout(G)
+        self.check_scale_and_center(vpos, scale=1, center=(0.5,0.5))
+        vpos = nx.spectral_layout(G)
+        self.check_scale_and_center(vpos, scale=1, center=(0.5,0.5))
+        vpos = nx.circular_layout(G)
+        self.check_scale_and_center(vpos, scale=2, center=(0,0))
+        vpos = nx.shell_layout(G)
+        self.check_scale_and_center(vpos, scale=2, center=(0,0))
+
+    def test_shell_layout(self):
+        G = nx.complete_graph(9)
+        shells=[[0], [1,2,3,5], [4,6,7,8]]
+        vpos = nx.shell_layout(G, nlist=shells)
+        vpos = nx.shell_layout(G, nlist=shells, scale=2, center=(3,4))
+        shells=[[0,1,2,3,5], [4,6,7,8]]
+        vpos = nx.shell_layout(G, nlist=shells)
+        vpos = nx.shell_layout(G, nlist=shells, scale=2, center=(3,4))
+
+    def test_spring_args(self):
+        G = nx.complete_graph(9)
+        vpos = nx.spring_layout(G, dim=3)
+        assert_equal(vpos[0].shape, (3,))
+        vpos = nx.spring_layout(G, fixed=[0,1], pos={1:(0,0), 2:(1,1)})
+        vpos = nx.spring_layout(G, k=2, fixed=[0,1], pos={1:(0,0), 2:(1,1)})
+        vpos = nx.spring_layout(G, scale=3, center=(2,5))
+        vpos = nx.spring_layout(G, scale=3)
+        vpos = nx.spring_layout(G, center=(2,5))
 
+    def test_spectral_for_small_graphs(self):
+        G = nx.Graph()
+        vpos = nx.spectral_layout(G)
+        vpos = nx.spectral_layout(G, center=(2,3))
+        G.add_node(0)
+        vpos = nx.spectral_layout(G)
+        vpos = nx.spectral_layout(G, center=(2,3))
+        G.add_node(1)
+        vpos = nx.spectral_layout(G)
+        vpos = nx.spectral_layout(G, center=(2,3))
+        # 3 nodes should allow eigensolvers to work
+        G.add_node(2)
+        vpos = nx.spectral_layout(G)
+        vpos = nx.spectral_layout(G, center=(2,3))
 
     def test_adjacency_interface_numpy(self):
         A=nx.to_numpy_matrix(self.Gs)