to_scipy_sparse_matrix

to_scipy_sparse_matrix(G, nodelist=None, dtype=None, weight='weight', format='csr')

Returns the graph adjacency matrix as a SciPy sparse matrix.

Parameters

Ggraph

The NetworkX graph used to construct the sparse matrix.

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 type of the matrix to be returned (default ‘csr’). For some algorithms different implementations of sparse matrices can perform better. See [1] for details.

Returns

ASciPy sparse matrix

Graph adjacency matrix.

Notes

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

The matrix entries 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 Scipy sparse matrix can be modified as follows:

>>> G = nx.Graph([(1, 1)])
>>> A = nx.to_scipy_sparse_matrix(G)
>>> print(A.todense())
[[1]]
>>> A.setdiag(A.diagonal() * 2)
>>> print(A.todense())
[[2]]

References

1

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

Examples

>>> G = nx.MultiDiGraph()
>>> G.add_edge(0, 1, weight=2)
0
>>> G.add_edge(1, 0)
0
>>> G.add_edge(2, 2, weight=3)
0
>>> G.add_edge(2, 2)
1
>>> S = nx.to_scipy_sparse_matrix(G, nodelist=[0, 1, 2])
>>> print(S.todense())
[[0 2 0]
 [1 0 0]
 [0 0 4]]