biadjacency_matrix#
- biadjacency_matrix(G, row_order, column_order=None, dtype=None, weight='weight', format='csr')[source]#
Returns the biadjacency matrix of the bipartite graph G.
Let
G = (U, V, E)
be a bipartite graph with node setsU = u_{1},...,u_{r}
andV = v_{1},...,v_{s}
. The biadjacency matrix [1] is ther
xs
matrixB
in whichb_{i,j} = 1
if, and only if,(u_i, v_j) in E
. If the parameterweight
is notNone
and matches the name of an edge attribute, its value is used instead of 1.- Parameters:
- Ggraph
A NetworkX graph
- row_orderlist of nodes
The rows of the matrix are ordered according to the list of nodes.
- column_orderlist, optional
The columns of the matrix are ordered according to the list of nodes. If column_order is None, then the ordering of columns is arbitrary.
- 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 data key used to provide each value in the matrix. If None, then each edge has weight 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 [2] for details.
- Returns:
- MSciPy sparse array
Biadjacency matrix representation of the bipartite graph G.
See also
adjacency_matrix
from_biadjacency_matrix
Notes
No attempt is made to check that the input graph is bipartite.
For directed bipartite graphs only successors are considered as neighbors. To obtain an adjacency matrix with ones (or weight values) for both predecessors and successors you have to generate two biadjacency matrices where the rows of one of them are the columns of the other, and then add one to the transpose of the other.
References
[2]Scipy Dev. References, “Sparse Matrices”, https://docs.scipy.org/doc/scipy/reference/sparse.html