# networkx.drawing.layout.spring_layout¶

spring_layout(G, k=None, pos=None, fixed=None, iterations=50, threshold=0.0001, 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. 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. 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 – A dictionary of positions keyed by node

Return type

dict

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)