wgOpdZddlZddlZddlmZddlZddlmZm Z gdZ ejddeddgdd Z e d ejd dd dd Z ejddd ddZejddddZejddddZe d ejddddZe d ejddddZe d ejddddZdZy)z0 Generators and functions for bipartite graphs. N)reduce)nodes_or_numberpy_random_state)configuration_modelhavel_hakimi_graphreverse_havel_hakimi_graphalternating_havel_hakimi_graphpreferential_attachment_graph random_graphgnmk_random_graphcomplete_bipartite_graphT)graphs returns_graphcjtjd|}|jrtjd|\}}|\}t |t j r-t |t j rDcgc]}||z c}|j|d|jdt|t|tzk7rtjd|jfd|Ddt|dtd |jd <|Scc}w) 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 supported bipartiterz,Inputs n1 and n2 must contain distinct nodesc34K|]}D]}||f ywN).0uvbottoms m/home/mcse/projects/flask/flask-venv/lib/python3.12/site-packages/networkx/algorithms/bipartite/generators.py z+complete_bipartite_graph..As!9&9QaV9V9szcomplete_bipartite_graph(z, )name) nx empty_graph is_directed NetworkXError isinstancenumbersIntegraladd_nodes_fromlenadd_edges_fromgraph)n1n2 create_usingGtopirs @rr r s: q,'A}}=>>GBJB"g&&'Jr7;K;K,L"()Q"q&)SA&Vq) 1vSCK''MNN9S991#c(2c&k]!LAGGFO H*s? D0bipartite_configuration_model)rrrcB tjd|tj}|jrtjdt |}t |}t |}t |}||k(stjd|d|t|||}t |dk(st|dk(r|St|D cgc] } | g|| z } } | D cgc] } | D]} |  c} } t|||zD cgc]} | g|| |z z} } | D cgc] } | D]} |  c} } |j |j|j fdt|Dd|_ |Scc} wcc} } wcc} wcc} } w)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),,c32K|]}||gywrr)rr0astubsbstubss rrz&configuration_model..sAfQi+Asr2) r r! MultiGraphr"r#r(sum_add_nodes_with_bipartite_labelmaxrangeshuffler)r)aseqbseqr-seedr.lenalenbsumasumbrstubssubseqxr9r:s @@rrrFsF q, >A}}=>> t9D t9D t9D t9D 4<=dV1TF K   (46A 4yA~Ta%*$K 0qaS47] 0E 0# 4FV 4a 4a 4F+0td{+C DaaS4D> ! DE D# 4FV 4a 4a 4F LLLLAU4[AA ,AF H 1 4 D 4sF )FF(Fbipartite_havel_hakimi_graphc<tjd|tj}|jrtjdt |}t |}t |}t |}||k(stjd|d|t|||}t |dk(st|dk(r|St|Dcgc] }|||g } }t|||zDcgc] }|||z |g} }| j| ru| j\} } | dk(rn\| j| | dD]@} | d}|j| || dxxdzcc<| ddk(s0| j| B| rud|_|Scc}wcc}w) 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 rr4rr6r7NrrKr r!r;r"r#r(r<r=r>r?sortpopadd_edgeremover)rArBr-r.naseqnbseqrFrGrr9r:degreertargets rrrsB q, >A}}=>> IE IE t9D t9D 4<=dV1TF K   (5%8A 4yA~Ta%*%L 1qtAwl 1F 1,1%,G HqtAI" HF H KKM jjl  Q;  fWX& &Fq A JJq!  1INIayA~ f%  & ,AF H#2 Hs F1Fc:tjd|tj}|jrtjdt |}t |}t |}t |}||k(stjd|d|t|||}t |dk(st|dk(r|St|Dcgc] }|||g } }t|||zDcgc] }|||z |g} }| j| j| rd| j\} } | dk(rnK| d| D]@} | d}|j| || dxxdzcc<| ddk(s0| j| B| rdd|_|Scc}wcc}w)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 rr4rr6r7r$bipartite_reverse_havel_hakimi_graphrM)rArBr-r.rDrErFrGrr9r:rTrrUs rrrsB q, >A}}=>> t9D t9D t9D t9D 4<=dV1TF K   (46A 4yA~Ta%*$K 0qtAwl 0F 0+0td{+C DatAH~q! DF D KKM KKM jjl  Q; Qv& &Fq A JJq!  1INIayA~ f%  & 4AF H#1 Ds F1Fc0tjd|tj}|jrtjdt |}t |}t |}t |}||k(stjd|d|t|||}t |dk(st|dk(r|St|Dcgc] }|||g } }t|||zDcgc] }|||z |g} }| r| j| j\} } | dk(rn| j| d| dz} | | | dzzd}t|| Dcgc] }|D]}| }}}t |t | t |zkr|j|j|D]@}|d}|j| ||dxxdzcc<|ddk(s0| j|B| rd |_|Scc}wcc}wcc}}w) aReturns a bipartite graph from two given degree sequences using an alternating Havel-Hakimi style construction. The graph is composed of two partitions. Set A has nodes 0 to (len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1). Nodes from the set A are connected to nodes in the set B by connecting the highest degree nodes in set A to alternatively the highest and the lowest degree nodes in set B until all stubs are connected. Parameters ---------- aseq : list Degree sequence for node set A. bseq : list Degree sequence for node set B. create_using : NetworkX graph instance, optional Return graph of this type. Notes ----- The sum of the two sequences must be equal: sum(aseq)=sum(bseq) If no graph type is specified use MultiGraph with parallel edges. If you want a graph with no parallel edges use create_using=Graph() but then the resulting degree sequences might not be exact. The nodes are assigned the attribute 'bipartite' with the value 0 or 1 to indicate which bipartite set the node belongs to. This function is not imported in the main namespace. To use it use nx.bipartite.alternating_havel_hakimi_graph rr4rr6r7Nr(bipartite_alternating_havel_hakimi_graph)r r!r;r"r#r(r<r=r>r?rNrOzipappendrPrQr)rArBr-r.rRrSrFrGrr9r:rTrsmalllargezrJrHrUs rr r #s D q, >A}}=>> IE IE t9D t9D 4<=dV1TF K   (5%8A 4yA~Ta$)%L 1qtAwl 1F 1,1%,G HqtAI" HF H  jjl  Q;  q6Q;'&A+-01u-9qq9!999 u:E SZ/ / LL % &Fq A JJq!  1INIayA~ f%  & $8AF H+2 H:sH1H "Hctjd|tj}|jrtjd|dkDrtjd|dt |}t ||d}t|Dcgc] }|g||z }}|r |dr|dd}|dj||j|kst ||k(r1t |} |j| d|j|| nxt|t |D cgc]} | g|j| z} } td| } |j| } |j| d|j|| |dr|j|d|r d |_|Scc}wcc} w) 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 rr4rrz probability z > 1rc ||zSrr)rJys rz/preferential_attachment_graph..s a!e'bipartite_preferential_attachment_model)r r!r;r"r#r(r=r?rQrandomadd_noderPrTrchoicer) rApr-rCr.rRrvvsourcerUbbbbbstubss rr r qsR q, >A}}=>>1uaS566 IE'5!4A!&u .A1#Q- .B . eU1XF qELL {{}q CFeOQ 6Q / 66*16uc!f1EFAqcAHHQK'FF !3R8W- 6Q / 66*e "Q%! "7AF H' /Gs F6.F;ctj}t|||}|rtj|}d|d|d|d|_|dkr|S|dk\rtj ||St jd|z }d}d}||kryt jd|jz } |dzt| |z z}||k\r||kr||z }|dz}||k\r||kr||kr|j|||z||kry|rd}d}||kryt jd|jz } |dzt| |z z}||k\r||kr||z }|dz}||k\r||kr||kr|j||z|||kry|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(r7rrrg?) r Graphr=DiGraphrr mathlogrfintrP) nmrirCdirectedr.lprwlrs rr r s\  A'1a0A JJqM%aS!AaS 2AFAvAv**1a00 #' B A A a% XXcDKKM) * ECRL 1fQAAAA1fQ q5 JJq!a%  a%  !e# -.BABG $Aq&QUEEq&QU1u 1q5!$!e Hrdc6tj}t|||}|rtj|}d|d|d|d|_|dk(s|dk(r|S||z}||k\rtj |||S|j dDcgc]\}}|dd k(s|}}}tt|t|z } d } | |krG|j|} |j| } | || vr/|j| | | dz } | |krG|Scc}}w) 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(r7rr)r-T)datarr) r rqr=rrrr nodeslistsetrhrP) rvrwkrCrxr. max_edgesdr/r edge_countrrs rr r s(Z  A'1a0A JJqM*1#Qqc1#Q 7AFAvaAII~**1aa@@d+ CAq~/B1 CC C #a&3s8# $FJ q. KK  KK  !9  JJq!  !OJ q. H Ds DDc |jt||zttt|dg|z}|j ttt|||zdg|zt j ||d|S)Nrrr)r'r?dictr[updater set_node_attributes)r.rDrErls rr=r=WstU4$;'( StqcDj )*AHHT#eD$+.d ; <=1a- Hrdr)NN)NF)__doc__rsr% functoolsrnetworkxr networkx.utilsrr__all__ _dispatchabler rrrr r r r r=rrdrrs ; T2!Q) 3) X6tSWXC YC L5dRVWG XG TT2F 3F RT2J 3J ZT2C 3C LT2R 3R jT2B 3B J rd