""" ==================== Biadjacency matrices ==================== """ import itertools import networkx as nx from networkx.convert_matrix import _generate_weighted_edges __all__ = ["biadjacency_matrix", "from_biadjacency_matrix"] @nx._dispatchable(edge_attrs="weight") def biadjacency_matrix( G, row_order, column_order=None, dtype=None, weight="weight", format="csr" ): r"""Returns the biadjacency matrix of the bipartite graph G. Let `G = (U, V, E)` be a bipartite graph with node sets `U = u_{1},...,u_{r}` and `V = v_{1},...,v_{s}`. The biadjacency matrix [1]_ is the `r` x `s` matrix `B` in which `b_{i,j} = 1` if, and only if, `(u_i, v_j) \in E`. If the parameter `weight` is not `None` and matches the name of an edge attribute, its value is used instead of 1. Parameters ---------- G : graph A NetworkX graph row_order : list of nodes The rows of the matrix are ordered according to the list of nodes. column_order : list, 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. dtype : NumPy data-type, optional A valid NumPy dtype used to initialize the array. If None, then the NumPy default is used. weight : string 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. format : str in {'dense', '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 ------- M : SciPy sparse array Biadjacency matrix representation of the bipartite graph G. 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. See Also -------- adjacency_matrix from_biadjacency_matrix References ---------- .. [1] https://en.wikipedia.org/wiki/Adjacency_matrix#Adjacency_matrix_of_a_bipartite_graph .. [2] Scipy Dev. References, "Sparse Matrices", https://docs.scipy.org/doc/scipy/reference/sparse.html """ import scipy as sp nlen = len(row_order) if nlen == 0: raise nx.NetworkXError("row_order is empty list") if len(row_order) != len(set(row_order)): msg = "Ambiguous ordering: `row_order` contained duplicates." raise nx.NetworkXError(msg) if column_order is None: column_order = list(set(G) - set(row_order)) mlen = len(column_order) if len(column_order) != len(set(column_order)): msg = "Ambiguous ordering: `column_order` contained duplicates." raise nx.NetworkXError(msg) row_index = dict(zip(row_order, itertools.count())) col_index = dict(zip(column_order, itertools.count())) if G.number_of_edges() == 0: row, col, data = [], [], [] else: row, col, data = zip( *( (row_index[u], col_index[v], d.get(weight, 1)) for u, v, d in G.edges(row_order, data=True) if u in row_index and v in col_index ) ) A = sp.sparse.coo_array((data, (row, col)), shape=(nlen, mlen), dtype=dtype) try: return A.asformat(format) except ValueError as err: raise nx.NetworkXError(f"Unknown sparse array format: {format}") from err @nx._dispatchable(graphs=None, returns_graph=True) def from_biadjacency_matrix( A, create_using=None, edge_attribute="weight", *, row_order=None, column_order=None, ): r"""Creates a new bipartite graph from a biadjacency matrix given as a SciPy sparse array. Parameters ---------- A : scipy sparse array A biadjacency matrix representation of a graph create_using : NetworkX graph Use specified graph for result. The default is Graph() edge_attribute : string Name of edge attribute to store matrix numeric value. The data will have the same type as the matrix entry (int, float, (real,imag)). row_order : list, optional (default: range(number of rows in `A`)) A list of the nodes represented by the rows of the matrix `A`. Will be represented in the graph as nodes with the `bipartite` attribute set to 0. Must be the same length as the number of rows in `A`. column_order : list, optional (default: range(number of columns in `A`)) A list of the nodes represented by the columns of the matrix `A`. Will be represented in the graph as nodes with the `bipartite` attribute set to 1. Must be the same length as the number of columns in `A`. Returns ------- G : NetworkX graph A bipartite graph with edges from the biadjacency matrix `A`, and nodes from `row_order` and `column_order`. Raises ------ ValueError If `row_order` or `column_order` are provided and are not the same length as the number of rows or columns in `A`, respectively. Notes ----- The nodes are labeled with the attribute `bipartite` set to an integer 0 or 1 representing membership in the `top` set (`bipartite=0`) or `bottom` set (`bipartite=1`) of the bipartite graph. If `create_using` is an instance of :class:`networkx.MultiGraph` or :class:`networkx.MultiDiGraph` and the entries of `A` are of type :class:`int`, then this function returns a multigraph (of the same type as `create_using`) with parallel edges. In this case, `edge_attribute` will be ignored. See Also -------- biadjacency_matrix from_numpy_array References ---------- [1] https://en.wikipedia.org/wiki/Adjacency_matrix#Adjacency_matrix_of_a_bipartite_graph """ G = nx.empty_graph(0, create_using) n, m = A.shape # Check/set row_order and column_order to have correct length and default values row_order, column_order = _validate_initialize_bipartite_nodelists( A, row_order, column_order ) # Make sure we get even the isolated nodes of the graph. G.add_nodes_from(range(n), bipartite=0) G.add_nodes_from(range(n, n + m), bipartite=1) # Create an iterable over (u, v, w) triples and for each triple, add an # edge from u to v with weight w. triples = ((u, n + v, d) for (u, v, d) in _generate_weighted_edges(A)) # If the entries in the adjacency matrix are integers and the graph is a # multigraph, then create parallel edges, each with weight 1, for each # entry in the adjacency matrix. Otherwise, create one edge for each # positive entry in the adjacency matrix and set the weight of that edge to # be the entry in the matrix. if A.dtype.kind in ("i", "u") and G.is_multigraph(): chain = itertools.chain.from_iterable triples = chain(((u, v, 1) for d in range(w)) for (u, v, w) in triples) G.add_weighted_edges_from(triples, weight=edge_attribute) # If the user provided nodelists, relabel the nodes of the graph inplace mapping = dict( itertools.chain(zip(range(n), row_order), zip(range(n, n + m), column_order)) ) if len(mapping): nx.relabel_nodes(G, mapping, copy=False) return G def _validate_initialize_bipartite_nodelists(A, row_order, column_order): n, m = A.shape # Validate nodelists if provided if row_order is not None: if len(row_order) != n: raise ValueError( "Length of row_order does not match number of rows in A ({n})" ) else: row_order = [] if column_order is not None: if len(column_order) != m: raise ValueError( "Length of column_order does not match number of columns in A ({m})" ) else: column_order = [] return row_order, column_order