9i SrSSKrSSKrSSKJr SS/r\R"SS9SSj5r\R"SS S 9SSSS .S jj5r S r g)z@ ==================== Biadjacency matrices ==================== N)_generate_weighted_edgesbiadjacency_matrixfrom_biadjacency_matrixweight) edge_attrscv^^^SSKn[U5nUS:Xa[R"S5e[U5[[ U55:waSn[R"U5eUc [ [ U5[ U5- 5n[U5n [U5[[ U55:waSn[R"U5e[ [U[R"555m[ [U[R"555mUR5S:Xa///pn O%[UUU4SjURUSS956upn URRXU 44Xy4US 9n U RU5$![an[R"S U35UeSnAff=f) aReturns 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 rNzrow_order is empty listz5Ambiguous ordering: `row_order` contained duplicates.z8Ambiguous ordering: `column_order` contained duplicates.c3># UH3upnUT;dMUT;dMTUTUURTS54v M5 g7fN)get).0uvd col_index row_indexrs d/var/www/html/land-doc-ocr/venv/lib/python3.13/site-packages/networkx/algorithms/bipartite/matrix.py %biadjacency_matrix..esK?&'9n?1y|QUU61-=>>">T)data)shapedtypezUnknown sparse array format: )scipylennx NetworkXErrorsetlistdictzip itertoolscountnumber_of_edgesedgessparse coo_arrayasformat ValueError)G row_order column_orderrrformatspnlenmsgmlenrowcolrAerrrrs ` @@rrrs@ y>D qy899 9~S^,,Es##CFS^34 | D <CL 122Hs##SIOO$567ISy'89:IaR$$ wwytw< $ T:.tl%PARzz&!! R!>vhGHcQRs>F F8F33F8T)graphs returns_graph)r*r+c ^ [R"SU5nURum n[XU5up4UR [ T 5SS9 UR [ T T U-5SS9 U 4Sj[ U55nURRS;a>UR5(a)[RRnU"SU55nURXrS9 [[R"[[ T 5U5[[ T T U-5U555n [!U 5(a[R""XYSS 9 U$) aCreates 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 r) bipartiter c38># UHupo1TU-U4v M g7f)N)r rrrns rr*from_biadjacency_matrix..sJ.I!1q5!}.Is)irc3Z^^# UHummnUU4Sj[U55v M! g7f)c3.># UH nTTS4v M g7fr r:)r rrrs rr4from_biadjacency_matrix...s5Hq!QHsN)range)r wrrs @@rrr<s$Ow)1a5E!H55ws'+)rF)copy)r empty_graphr(_validate_initialize_bipartite_nodelistsadd_nodes_fromrArrkind is_multigraphr!chain from_iterableadd_weighted_edges_fromrr r relabel_nodes) r3 create_usingedge_attributer*r+r)mtriplesrImappingr;s @rrrrs"F q,'A 77DAqF lI U1X+U1a!e_2K.Fq.IJG  ww||z!aoo&7&7--OwOOg=E!Hi0#eAq1uo|2TUG 7|| %0 HcURup4Ub[U5U:wa [S5eO/nUb[U5U:wa [S5eX4$/nX4$)NzQ N     |  !T  "  ""  ""rR)NNrcsr)Nr) __doc__r!networkxrnetworkx.convert_matrixr__all__ _dispatchablerrrEr:rRrrZs < !: ;X&IN_R'_RDT2_  _ 3_ D#rR