o ёh╫Oу@s<dZddlZddlZddlmZddlZddlmZm Z gdвZ ejdddНeddgГd d d ДГГZe dГejdddd Нd!ddДГГZ ejdddd Нd ddДГZejdddНd ddДГZejdddНd ddДГZe dГejdddНd!ddДГГZe dГejdddНd"ddДГГZe dГejdddНd"ddДГГZddДZdS)#z0 Generators and functions for bipartite graphs. щN)┌reduce)┌nodes_or_number┌py_random_state)┌configuration_model┌havel_hakimi_graph┌reverse_havel_hakimi_graph┌alternating_havel_hakimi_graph┌preferential_attachment_graph┌random_graph┌gnmk_random_graph┌complete_bipartite_graphT)┌graphs┌ returns_graphщcs╥tаd|б}|абrtаdбВИ\Й}|\}ЙtИtjГr,t|tjГr,ЗfddДИDГЙ|j|ddН|jИddНt|Гt|ГtИГkrKtаdбВ|а Зfdd Д|DГбd t|ГЫdtИГЫdЭ|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 r·Directed Graph not supportedcsg|]}И|СqSйrй┌.0┌i)┌n1r·\/var/www/vscode/kcb/lib/python3.10/site-packages/networkx/algorithms/bipartite/generators.py┌ <sz,complete_bipartite_graph..й┌ bipartiterz,Inputs n1 and n2 must contain distinct nodesc3s"Б|]}ИD]}||fVqqdSйNr)r┌u┌v)┌bottomrr┌ AsА z+complete_bipartite_graph..zcomplete_bipartite_graph(z, ·)┌name)┌nx┌empty_graph┌is_directed┌ NetworkXError┌ isinstance┌numbers┌Integral┌add_nodes_from┌len┌add_edges_from┌graph)r┌n2┌create_using┌G┌topr)rrrrs rщ┌bipartite_configuration_model)r r rc stjd|tjdН}|абrtаdбВtИГЙtИГ}tИГ}tИГ}||ks1tаd|Ыd|ЫЭбВt|И|Г}tИГdksCtИГdkrE|SЗfddДt ИГDГ}ddД|DГЙЗЗfd dДt ИИ|ГDГ}d dД|DГЙ|а Иб|а Иб|аЗЗfddДt |ГDГбd |_|S)aуReturns 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 rй┌defaultr·/invalid degree sequences, sum(aseq)!=sum(bseq),·,cєg|] }|gИ|СqSrrйrrй┌aseqrrr~єz'configuration_model..cSєg|] }|D]}|СqqSrrйr┌subseq┌xrrrrr:csg|]}|gИ|ИСqSrrr7й┌bseq┌lenarrrБscSr;rrr<rrrrВr:c3s Б|]}И|И|gVqdSrrr)┌astubs┌bstubsrrrИsАz&configuration_model..r1) r!r"┌ MultiGraphr#r$r)┌sum┌_add_nodes_with_bipartite_label┌max┌range┌shuffler*r ) r9r@r-┌seedr.┌lenb┌suma┌sumb┌stubsr)r9rBr@rCrArrFs.# r┌bipartite_havel_hakimi_graphc sDtjd|tjdН}|абrtаdбВtИГЙtИГ}tИГ}tИГ}||ks1tаd|Ыd|ЫЭбВt|И|Г}tИГdksCtИГdkrE|SЗfddДt ИГDГ}ЗЗfddДt ИИ|ГDГ}|а б|rЭ|аб\} } | dkrpn-|а б|| d ЕD]}|d }|а| |б|dd 8<|ddkrЪ|а |бq{|sed|_|S)aйReturns a bipartite graph from two given degree sequences using a Havel-Hakimi style construction. The graph is composed of two partitions. Set A has nodes 0 to (len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1). Nodes from the set A are connected to nodes in the set B by connecting the highest degree nodes in set A to the highest degree nodes in set B until all stubs are connected. Parameters ---------- aseq : list Degree sequence for node set A. bseq : list Degree sequence for node set B. create_using : NetworkX graph instance, optional Return graph of this type. Notes ----- The sum of the two sequences must be equal: sum(aseq)=sum(bseq) If no graph type is specified use MultiGraph with parallel edges. If you want a graph with no parallel edges use create_using=Graph() but then the resulting degree sequences might not be exact. The nodes are assigned the attribute 'bipartite' with the value 0 or 1 to indicate which bipartite set the node belongs to. This function is not imported in the main namespace. To use it use nx.bipartite.havel_hakimi_graph rr2rr4r5cєg|]}И||gСqSrrr7r8rrr┼єz&havel_hakimi_graph..cєg|] }И|И|gСqSrrr7йr@┌naseqrrr╞єNrrOйr!r"rDr#r$r)rErFrGrH┌sort┌pop┌add_edge┌remover ) r9r@r-r.┌nbseqrLrMrBrC┌degreer┌targetrrйr9r@rTrrОs@! Аї rc sBtjd|tjdН}|абrtаdбВtИГЙtИГ}tИГ}tИГ}||ks1tаd|Ыd|ЫЭбВt|И|Г}tИГdksCtИГdkrE|SЗfddДt ИГDГ}ЗЗfddДt ИИ|ГDГ}|а б|а б|rЬ|аб\} } | dkrtn(|d| ЕD]}|d }|а| |б|dd 8<|ddkrЩ|а |бqz|sid |_|S)aмReturns 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 rr2rr4r5crPrrr7r8rrrrQz.reverse_havel_hakimi_graph..crRrrr7r?rrrrUr┌$bipartite_reverse_havel_hakimi_graphrV) r9r@r-r.rKrLrMrBrCr\rr]rr)r9r@rArr┘s@! АЎrcsЪtjd|tjdН}|абrtаdбВtИГЙtИГ}tИГ}tИГ}||ks1tаd|Ыd|ЫЭбВt|И|Г}tИГdksCtИГdkrE|SЗfddДt ИГDГ}ЗЗfddДt ИИ|ГDГ}|r╚|а б|аб\} } | dkrpnX|а б|d| d Е}|| | d d Е}ddДt||ГDГ} t| Гt|Гt|Гkrд| а |абб| D]}|d}|а| |б|dd8<|ddkr┼|а|бqж|sad |_|S)aуReturns a bipartite graph from two given degree sequences using an alternating Havel-Hakimi style construction. The graph is composed of two partitions. Set A has nodes 0 to (len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1). Nodes from the set A are connected to nodes in the set B by connecting the highest degree nodes in set A to alternatively the highest and the lowest degree nodes in set B until all stubs are connected. Parameters ---------- aseq : list Degree sequence for node set A. bseq : list Degree sequence for node set B. create_using : NetworkX graph instance, optional Return graph of this type. Notes ----- The sum of the two sequences must be equal: sum(aseq)=sum(bseq) If no graph type is specified use MultiGraph with parallel edges. If you want a graph with no parallel edges use create_using=Graph() but then the resulting degree sequences might not be exact. The nodes are assigned the attribute 'bipartite' with the value 0 or 1 to indicate which bipartite set the node belongs to. This function is not imported in the main namespace. To use it use nx.bipartite.alternating_havel_hakimi_graph rr2rr4r5crPrrr7r8rrrYrQz2alternating_havel_hakimi_graph..crRrrr7rSrrrZrUщNcSr;rr)r┌zr>rrrrcr:r┌(bipartite_alternating_havel_hakimi_graph)r!r"rDr#r$r)rErFrGrHrWrX┌zip┌appendrYrZr )r9r@r-r.r[rLrMrBrCr\r┌small┌largerNr]rrr^rr#sJ" АЁrc s<tjd|tjdНЙИабrtаdбВ|dkrtаd|ЫdЭбВtИГ}tИ|dГЙЗfddДt|ГDГ}|rЩ|drР|dd}|dа|б|а б|ksStИГ|kretИГ}Иj |dd НИа||бn'Зfd dДt|tИГГDГ}tddД|Г} |а | б}Иj |dd НИа||б|ds:|а|dб|s6d И_ИS)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 rr2rrzprobability z > 1cr6rrr7r8rrrгr:z1preferential_attachment_graph..rcsg|] }|gИа|бСqSr)r\)r┌b)r.rrrнrUcSs||Srr)r>┌yrrr┌пsz/preferential_attachment_graph..┌'bipartite_preferential_attachment_model)r!r"rDr#r$r)rFrHrZ┌random┌add_noderYr┌choicer ) r9┌pr-rJrT┌vv┌sourcer]┌bb┌bbstubsr)r.r9rr qs4) ЄЁr Fc Cs~tаб}t|||Г}|rtа|б}d|Ыd|Ыd|ЫdЭ|_|dkr$|S|dkr.tа||бStаd|б}d}d}||krxtаd|абб} |dt | |Г}||krh||krh||}|d}||krh||ksX||krt|а |||б||ks=|r╜d}d}||kr╜tаd|абб} |dt | |Г}||krн||krн||}|d}||krн||ksЭ||kr╣|а |||б||ksВ|S)uoReturns a bipartite random graph. This is a bipartite version of the binomial (Erd┼Сs-R├йnyi) 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(r5rrrgЁ?щ )r!┌GraphrF┌DiGraphr r┌math┌logrk┌intrY) ┌n┌mrnrJ┌directedr.┌lpr┌w┌lrrrrr ╣sH. ■∙ ■∙ r cCsшtаб}t|||Г}|rtа|б}d|Ыd|Ыd|ЫdЭ|_|dks&|dkr(|S||}||kr8tj|||dНSddД|jdd НDГ}tt|Гt|ГГ}d } | |krr|а |б} |а |б}||| vrdqO|а | |б| d7} | |ksS|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(r5rr)r-cSs g|]\}}|ddkr|СqS)rrr)rry┌drrrrHs z%gnmk_random_graph..T)┌datar)r!rtrFrur r┌nodes┌list┌setrmrY)ryrz┌krJr{r.┌ max_edgesr/r┌ edge_countrrrrrrs,- ° rcCs`|аt||Гбttt|Гdg|ГГ}|аttt|||Гdg|ГГбtа||dб|S)Nrrr)r(rH┌dictrc┌updater!┌set_node_attributes)r.rArKrgrrrrFWs $rFr)NN)NF)┌__doc__rvr&┌ functoolsr┌networkxr!┌networkx.utilsrr┌__all__┌ _dispatchablerrrrrr r rrFrrrr┌s: ,FJIMFUE