to_scipy_sparse_array#

to_scipy_sparse_array(G, nodelist=None, dtype=None, weight='weight', format='csr')[source]#

Returns the graph adjacency matrix as a SciPy sparse array.

Parameters:

Ggraph: The NetworkX graph used to construct the sparse array.
nodelistlist, optional: The rows and columns are ordered according to the nodes in nodelist. If nodelist is None, then the ordering is produced by G.nodes().
dtypeNumPy data-type, optional: A valid NumPy dtype used to initialize the array. If None, then the NumPy default is used.
weightstring 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.
formatstr in {‘bsr’, ‘csr’, ‘csc’, ‘coo’, ‘lil’, ‘dia’, ‘dok’}: The format of the sparse array to be returned (default ‘csr’). For some algorithms different implementations of sparse arrays can perform better. See [1] for details.

Returns:

ASciPy sparse array: Graph adjacency matrix.

Notes

For directed graphs, matrix entry i, j corresponds to an edge from i to j.

The values of the adjacency matrix are populated using the edge attribute held in parameter weight. When an edge does not have that attribute, the value of the entry is 1.

For multiple edges the matrix values are the sums of the edge weights.

When nodelist does not contain every node in G, the adjacency matrix is built from the subgraph of G that is induced by the nodes in nodelist.

The convention used for self-loop edges in graphs is to assign the diagonal matrix entry value to the weight attribute of the edge (or the number 1 if the edge has no weight attribute). If the alternate convention of doubling the edge weight is desired the resulting array can be modified as follows:

>>> G = nx.Graph([(1, 1)])
>>> A = nx.to_scipy_sparse_array(G)
>>> A.toarray()
array([[1]])
>>> A.setdiag(A.diagonal() * 2)
>>> A.toarray()
array([[2]])

References

[1]

Scipy Dev. References, “Sparse Arrays”, https://docs.scipy.org/doc/scipy/reference/sparse.html

Examples

Basic usage:

>>> G = nx.path_graph(4)
>>> A = nx.to_scipy_sparse_array(G)
>>> A  
<Compressed Sparse Row sparse array of dtype 'int64'
    with 6 stored elements and shape (4, 4)>

>>> A.toarray()
array([[0, 1, 0, 0],
       [1, 0, 1, 0],
       [0, 1, 0, 1],
       [0, 0, 1, 0]])

Note

The toarray method is used in these examples to better visualize the adjacancy matrix. For a dense representation of the adjaceny matrix, use to_numpy_array instead.

Directed graphs:

>>> G = nx.DiGraph([(0, 1), (1, 2), (2, 3)])
>>> nx.to_scipy_sparse_array(G).toarray()
array([[0, 1, 0, 0],
       [0, 0, 1, 0],
       [0, 0, 0, 1],
       [0, 0, 0, 0]])

>>> H = G.reverse()
>>> H.edges
OutEdgeView([(1, 0), (2, 1), (3, 2)])
>>> nx.to_scipy_sparse_array(H).toarray()
array([[0, 0, 0, 0],
       [1, 0, 0, 0],
       [0, 1, 0, 0],
       [0, 0, 1, 0]])

By default, the order of the rows/columns of the adjacency matrix is determined by the ordering of the nodes in G:

>>> G = nx.Graph()
>>> G.add_nodes_from([3, 5, 0, 1])
>>> G.add_edges_from([(1, 3), (1, 5)])
>>> nx.to_scipy_sparse_array(G).toarray()
array([[0, 0, 0, 1],
       [0, 0, 0, 1],
       [0, 0, 0, 0],
       [1, 1, 0, 0]])

The ordering of the rows can be changed with nodelist:

>>> ordered = [0, 1, 3, 5]
>>> nx.to_scipy_sparse_array(G, nodelist=ordered).toarray()
array([[0, 0, 0, 0],
       [0, 0, 1, 1],
       [0, 1, 0, 0],
       [0, 1, 0, 0]])

If nodelist contains a subset of the nodes in G, the adjacency matrix for the node-induced subgraph is produced:

>>> nx.to_scipy_sparse_array(G, nodelist=[1, 3, 5]).toarray()
array([[0, 1, 1],
       [1, 0, 0],
       [1, 0, 0]])

The values of the adjacency matrix are drawn from the edge attribute specified by the weight parameter:

>>> G = nx.path_graph(4)
>>> nx.set_edge_attributes(
...     G, values={(0, 1): 1, (1, 2): 10, (2, 3): 2}, name="weight"
... )
>>> nx.set_edge_attributes(
...     G, values={(0, 1): 50, (1, 2): 35, (2, 3): 10}, name="capacity"
... )
>>> nx.to_scipy_sparse_array(G).toarray()  # Default weight="weight"
array([[ 0,  1,  0,  0],
       [ 1,  0, 10,  0],
       [ 0, 10,  0,  2],
       [ 0,  0,  2,  0]])
>>> nx.to_scipy_sparse_array(G, weight="capacity").toarray()
array([[ 0, 50,  0,  0],
       [50,  0, 35,  0],
       [ 0, 35,  0, 10],
       [ 0,  0, 10,  0]])

Any edges that don’t have a weight attribute default to 1:

>>> G[1][2].pop("capacity")
35
>>> nx.to_scipy_sparse_array(G, weight="capacity").toarray()
array([[ 0, 50,  0,  0],
       [50,  0,  1,  0],
       [ 0,  1,  0, 10],
       [ 0,  0, 10,  0]])

When G is a multigraph, the values in the adjacency matrix are given by the sum of the weight edge attribute over each edge key:

>>> G = nx.MultiDiGraph([(0, 1), (0, 1), (0, 1), (2, 0)])
>>> nx.to_scipy_sparse_array(G).toarray()
array([[0, 3, 0],
       [0, 0, 0],
       [1, 0, 0]])