U ?hM@sdZddlZddlZddlmZddlZddlmZm Z ddddd d d d gZ edd gddd Z e ddddZ dddZ dddZdddZe dddd Ze dd dd Ze dd!dd ZddZdS)"z0 Generators and functions for bipartite graphs. N)reduce)nodes_or_numberpy_random_stateconfiguration_modelhavel_hakimi_graphreverse_havel_hakimi_graphalternating_havel_hakimi_graphpreferential_attachment_graph random_graphgnmk_random_graphcomplete_bipartite_graphcstd|}|rtd\}|\}ttjrXt|tjrXfddD|j|dd|jddt|t|tkrtd| fdd |Dd d |d |j d <|S)aReturns the complete bipartite graph `K_{n_1,n_2}`. The graph is composed of two partitions with nodes 0 to (n1 - 1) in the first and nodes n1 to (n1 + n2 - 1) in the second. Each node in the first is connected to each node in the second. Parameters ---------- n1, n2 : integer or iterable container of nodes If integers, nodes are from `range(n1)` and `range(n1, n1 + n2)`. If a container, the elements are the nodes. create_using : NetworkX graph instance, (default: nx.Graph) Return graph of this type. Notes ----- Nodes are the integers 0 to `n1 + n2 - 1` unless either n1 or n2 are containers of nodes. If only one of n1 or n2 are integers, that integer is replaced by `range` of that integer. The nodes are assigned the attribute 'bipartite' with the value 0 or 1 to indicate which bipartite set the node belongs to. This function is not imported in the main namespace. To use it use nx.bipartite.complete_bipartite_graph rDirected Graph not supportedcsg|] }|qSr.0i)n1rZ/var/www/html/venv/lib/python3.8/site-packages/networkx/algorithms/bipartite/generators.py :sz,complete_bipartite_graph.. bipartiter z,Inputs n1 and n2 must contain distinct nodesc3s |]}D]}||fVq qdSNr)ruv)bottomrr ?sz+complete_bipartite_graph..zcomplete_bipartite_graph(z, )name) nx empty_graph is_directed NetworkXError isinstancenumbersIntegraladd_nodes_fromlenadd_edges_fromgraph)rZn2 create_usingGtopr)rrrr s   c stjd|tjd}|r$tdtt}t}t}||ksbtd|d|t||}tdkstdkr|Sfddt dD}dd|Dfd dt |D}d d|D| | | fd d t |Dd |_ |S)aReturns a random bipartite graph from two given degree sequences. Parameters ---------- aseq : list Degree sequence for node set A. bseq : list Degree sequence for node set B. create_using : NetworkX graph instance, optional Return graph of this type. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. The graph is composed of two partitions. Set A has nodes 0 to (len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1). Nodes from set A are connected to nodes in set B by choosing randomly from the possible free stubs, one in A and one in B. Notes ----- The sum of the two sequences must be equal: sum(aseq)=sum(bseq) If no graph type is specified use MultiGraph with parallel edges. If you want a graph with no parallel edges use create_using=Graph() but then the resulting degree sequences might not be exact. The nodes are assigned the attribute 'bipartite' with the value 0 or 1 to indicate which bipartite set the node belongs to. This function is not imported in the main namespace. To use it use nx.bipartite.configuration_model rdefaultr/invalid degree sequences, sum(aseq)!=sum(bseq),,csg|]}|g|qSrrrraseqrrr{sz'configuration_model..cSsg|]}|D]}|q qSrrrZsubseqxrrrr|scsg|]}|g|qSrrr2bseqlenarrr~scSsg|]}|D]}|q qSrrr5rrrrsc3s|]}||gVqdSrrr)astubsbstubsrrrsz&configuration_model..Zbipartite_configuration_model) rr MultiGraphr!r"r'sum_add_nodes_with_bipartite_labelmaxrangeshuffler(r) r4r8r*seedr+lenbsumasumbstubsr)r4r:r8r;r9rrDs."    c sHtjd|tjd}|r$tdtt}t}t}||ksbtd|d|t||}tdkstdkr|Sfddt dD}fddt |D}| |r>| \} } | dkrq>| || d D]>} | d } | | | | dd 8<| ddkr| | qqd |_|S) aReturns a bipartite graph from two given degree sequences using a Havel-Hakimi style construction. The graph is composed of two partitions. Set A has nodes 0 to (len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1). Nodes from the set A are connected to nodes in the set B by connecting the highest degree nodes in set A to the highest degree nodes in set B until all stubs are connected. Parameters ---------- aseq : list Degree sequence for node set A. bseq : list Degree sequence for node set B. create_using : NetworkX graph instance, optional Return graph of this type. Notes ----- The sum of the two sequences must be equal: sum(aseq)=sum(bseq) If no graph type is specified use MultiGraph with parallel edges. If you want a graph with no parallel edges use create_using=Graph() but then the resulting degree sequences might not be exact. The nodes are assigned the attribute 'bipartite' with the value 0 or 1 to indicate which bipartite set the node belongs to. This function is not imported in the main namespace. To use it use nx.bipartite.havel_hakimi_graph rr.rr0r1csg|]}||gqSrrr2r3rrrsz&havel_hakimi_graph..csg|]}||gqSrrr2r8naseqrrrsNr Zbipartite_havel_hakimi_graphrr r<r!r"r'r=r>r?r@sortpopadd_edgeremover) r4r8r*r+nbseqrDrEr:r;degreertargetrrr4r8rHrrs<      c sFtjd|tjd}|r$tdtt}t}t}||ksbtd|d|t||}tdkstdkr|Sfddt dD}fddt |D}| | |r<| \} } | dkrq<|d| D]>} | d } | | | | dd 8<| ddkr| | qqd |_|S) aReturns a bipartite graph from two given degree sequences using a Havel-Hakimi style construction. The graph is composed of two partitions. Set A has nodes 0 to (len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1). Nodes from set A are connected to nodes in the set B by connecting the highest degree nodes in set A to the lowest degree nodes in set B until all stubs are connected. Parameters ---------- aseq : list Degree sequence for node set A. bseq : list Degree sequence for node set B. create_using : NetworkX graph instance, optional Return graph of this type. Notes ----- The sum of the two sequences must be equal: sum(aseq)=sum(bseq) If no graph type is specified use MultiGraph with parallel edges. If you want a graph with no parallel edges use create_using=Graph() but then the resulting degree sequences might not be exact. The nodes are assigned the attribute 'bipartite' with the value 0 or 1 to indicate which bipartite set the node belongs to. This function is not imported in the main namespace. To use it use nx.bipartite.reverse_havel_hakimi_graph rr.rr0r1csg|]}||gqSrrr2r3rrr sz.reverse_havel_hakimi_graph..csg|]}||gqSrrr2r7rrr sr Z$bipartite_reverse_havel_hakimi_graphrI) r4r8r*r+rCrDrEr:r;rOrrPrr)r4r8r9rrs<      cstjd|tjd}|r$tdtt}t}t}||ksbtd|d|t||}tdkstdkr|Sfddt dD}fddt |D}|r| | \} } | dkrq| |d| d } || | d d } d dt | | D} t| t| t| krP| | | D]B}|d }|| ||dd 8<|ddkrT||qTqd |_|S)aReturns a bipartite graph from two given degree sequences using an alternating Havel-Hakimi style construction. The graph is composed of two partitions. Set A has nodes 0 to (len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1). Nodes from the set A are connected to nodes in the set B by connecting the highest degree nodes in set A to alternatively the highest and the lowest degree nodes in set B until all stubs are connected. Parameters ---------- aseq : list Degree sequence for node set A. bseq : list Degree sequence for node set B. create_using : NetworkX graph instance, optional Return graph of this type. Notes ----- The sum of the two sequences must be equal: sum(aseq)=sum(bseq) If no graph type is specified use MultiGraph with parallel edges. If you want a graph with no parallel edges use create_using=Graph() but then the resulting degree sequences might not be exact. The nodes are assigned the attribute 'bipartite' with the value 0 or 1 to indicate which bipartite set the node belongs to. This function is not imported in the main namespace. To use it use nx.bipartite.alternating_havel_hakimi_graph rr.rr0r1csg|]}||gqSrrr2r3rrrSsz2alternating_havel_hakimi_graph..csg|]}||gqSrrr2rGrrrTsNcSsg|]}|D]}|q qSrr)rzr6rrrr]sr Z(bipartite_alternating_havel_hakimi_graph)rr r<r!r"r'r=r>r?r@rJrKzipappendrLrMr)r4r8r*r+rNrDrEr:r;rOrZsmallZlargerFrPrrrQrrsF!    c s:tjd|tjdr$td|dkr>td|dt}t|dfddtd|D}|r0|dr |dd}|d|| |kst|krt}j |dd  ||qpfd dt|tD}t d d |} | | }j |dd  ||qp||dqjd _S)a^Create a bipartite graph with a preferential attachment model from a given single degree sequence. The graph is composed of two partitions. Set A has nodes 0 to (len(aseq) - 1) and set B has nodes starting with node len(aseq). The number of nodes in set B is random. Parameters ---------- aseq : list Degree sequence for node set A. p : float Probability that a new bottom node is added. create_using : NetworkX graph instance, optional Return graph of this type. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. References ---------- .. [1] Guillaume, J.L. and Latapy, M., Bipartite graphs as models of complex networks. Physica A: Statistical Mechanics and its Applications, 2006, 371(2), pp.795-813. .. [2] Jean-Loup Guillaume and Matthieu Latapy, Bipartite structure of all complex networks, Inf. Process. Lett. 90, 2004, pg. 215-221 https://doi.org/10.1016/j.ipl.2004.03.007 Notes ----- The nodes are assigned the attribute 'bipartite' with the value 0 or 1 to indicate which bipartite set the node belongs to. This function is not imported in the main namespace. To use it use nx.bipartite.preferential_attachment_graph rr.rr z probability z > 1csg|]}|g|qSrrr2r3rrrsz1preferential_attachment_graph..rcsg|]}|g|qSr)rO)rb)r+rrrscSs||Srr)r6yrrrz/preferential_attachment_graph..Z'bipartite_preferential_attachment_model)rr r<r!r"r'r>r@rMrandomadd_noderLrchoicer) r4pr*rBrHZvvsourcerPZbbZbbstubsr)r+r4rr ks0(     Fc Cs`t}t|||}|r"t|}d|d|d|d|_|dkrH|S|dkr\t||Std|}d}d}||krtd|} |dt | |}||kr||kr||}|d}q||krr| |||qr|r\d}d}||kr\td|} |dt | |}||krB||krB||}|d}q||kr| |||q|S)uoReturns a bipartite random graph. This is a bipartite version of the binomial (Erdős-Rényi) graph. The graph is composed of two partitions. Set A has nodes 0 to (n - 1) and set B has nodes n to (n + m - 1). Parameters ---------- n : int The number of nodes in the first bipartite set. m : int The number of nodes in the second bipartite set. p : float Probability for edge creation. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. directed : bool, optional (default=False) If True return a directed graph Notes ----- The bipartite random graph algorithm chooses each of the n*m (undirected) or 2*nm (directed) possible edges with probability p. This algorithm is $O(n+m)$ where $m$ is the expected number of edges. The nodes are assigned the attribute 'bipartite' with the value 0 or 1 to indicate which bipartite set the node belongs to. This function is not imported in the main namespace. To use it use nx.bipartite.random_graph See Also -------- gnp_random_graph, configuration_model References ---------- .. [1] Vladimir Batagelj and Ulrik Brandes, "Efficient generation of large random networks", Phys. Rev. E, 71, 036113, 2005. zfast_gnp_random_graph(r1rrr g?) rGraphr>DiGraphrr mathlogrZintrL) nmr]rBdirectedr+Zlprwlrrrrr s@-      c Cst}t|||}|r"t|}d|d|d|d|_|dksL|dkrP|S||}||krptj|||dSdd|jdd D}tt|t|}d } | |kr| |} | |} | || krqq| | | | d7} q|S) aReturns a random bipartite graph G_{n,m,k}. Produces a bipartite graph chosen randomly out of the set of all graphs with n top nodes, m bottom nodes, and k edges. The graph is composed of two sets of nodes. Set A has nodes 0 to (n - 1) and set B has nodes n to (n + m - 1). Parameters ---------- n : int The number of nodes in the first bipartite set. m : int The number of nodes in the second bipartite set. k : int The number of edges seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. directed : bool, optional (default=False) If True return a directed graph Examples -------- from nx.algorithms import bipartite G = bipartite.gnmk_random_graph(10,20,50) See Also -------- gnm_random_graph Notes ----- If k > m * n then a complete bipartite graph is returned. This graph is a bipartite version of the `G_{nm}` random graph model. The nodes are assigned the attribute 'bipartite' with the value 0 or 1 to indicate which bipartite set the node belongs to. This function is not imported in the main namespace. To use it use nx.bipartite.gnmk_random_graph zbipartite_gnm_random_graph(r1rr )r*cSs g|]\}}|ddkr|qS)rrr)rredrrrr?s z%gnmk_random_graph..T)datar) rr`r>rarr Znodeslistsetr\rL) rerfkrBrgr+Z max_edgesr,rZ edge_countrrrrrr s*,       cCsd|td||tttd|dg|}|ttt|||dg|t||d|S)Nrr r)r&r@dictrTupdaterZset_node_attributes)r+r9rCrVrrrr>Ns $r>)N)NN)N)N)N)NN)NF)NF)__doc__rbr$ functoolsrZnetworkxrZnetworkx.utilsrr__all__r rrrrr r r r>rrrrs8   , F J I M F U E