3 MdL@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_graphcstjd|}|jrtjd\}|\}t|tjrLfddD|j|dd|jdd|jfdd|Dd d |d |j d <|S) a)Returns 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 : integer Number of nodes for node set A. n2 : integer Number of nodes for node set B. create_using : NetworkX graph instance, optional Return graph of this type. Notes ----- Node labels are the integers 0 to `n_1 + n_2 - 1`. 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 rzDirected Graph not supportedcsg|] }|qSr).0i)n1rZ/var/www/html/virt/lib/python3.6/site-packages/networkx/algorithms/bipartite/generators.py 8sz,complete_bipartite_graph..) bipartiter c3s |]}D]}||fVq qdS)Nr)ruv)bottomrr ;sz+complete_bipartite_graph..zcomplete_bipartite_graph(,)name) nx empty_graph is_directed NetworkXError isinstancenumbersIntegraladd_nodes_fromadd_edges_fromgraph)rZn2 create_usingGtopr)rrrr s   c s4tjd|tjd}|jr$tjdtt}t}t}||ksbtjd|d|t||}tdkstdkr|Sg}|j fddt dDgdd|Dg}|j fd dt |Dgd d|D|j |j |j fd dt |Dd |_ |S) aReturns a random bipartite graph from two given degree sequences. Parameters ---------- aseq : list Degree sequence for node set A. bseq : list Degree sequence for node set B. create_using : NetworkX graph instance, optional Return graph of this type. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. The graph is composed of two partitions. Set A has nodes 0 to (len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1). Nodes from set A are connected to nodes in set B by choosing randomly from the possible free stubs, one in A and one in B. Notes ----- The sum of the two sequences must be equal: sum(aseq)=sum(bseq) If no graph type is specified use MultiGraph with parallel edges. If you want a graph with no parallel edges use create_using=Graph() but then the resulting degree sequences might not be exact. The nodes are assigned the attribute 'bipartite' with the value 0 or 1 to indicate which bipartite set the node belongs to. This function is not imported in the main namespace. To use it use nx.bipartite.configuration_model r)defaultzDirected Graph not supportedz/invalid degree sequences, sum(aseq)!=sum(bseq),rcsg|]}|g|qSrr)rr)aseqrrrxsz'configuration_model..cSsg|]}|D]}|q qSrr)rsubseqxrrrrzscsg|]}|g|qSrr)rr)bseqlenarrr}scSsg|]}|D]}|q qSrr)rr,r-rrrrscsg|]}||gqSrr)rr)astubsbstubsrrrsZbipartite_configuration_model)rr MultiGraphrrlensum_add_nodes_with_bipartite_labelmaxextendrangeshuffler$r) r+r.r&seedr'lenbsumasumbstubsr)r+r0r.r1r/rr@s4"  $  c sRtjd|tjd}|jr$tjdtt}t}t}||ksbtjd|d|t||}tdkstdkr|Sfddt dD}fddt |D}|j x~|rF|j \} } | dkrP|j xT|| d D]B} | d } |j | | | dd 8<| ddkr|j | qWqWd |_|S) aReturns a bipartite graph from two given degree sequences using a Havel-Hakimi style construction. The graph is composed of two partitions. Set A has nodes 0 to (len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1). Nodes from the set A are connected to nodes in the set B by connecting the highest degree nodes in set A to the highest degree nodes in set B until all stubs are connected. Parameters ---------- aseq : list Degree sequence for node set A. bseq : list Degree sequence for node set B. create_using : NetworkX graph instance, optional Return graph of this type. Notes ----- The sum of the two sequences must be equal: sum(aseq)=sum(bseq) If no graph type is specified use MultiGraph with parallel edges. If you want a graph with no parallel edges use create_using=Graph() but then the resulting degree sequences might not be exact. The nodes are assigned the attribute 'bipartite' with the value 0 or 1 to indicate which bipartite set the node belongs to. This function is not imported in the main namespace. To use it use nx.bipartite.havel_hakimi_graph r)r*zDirected Graph not supportedz/invalid degree sequences, sum(aseq)!=sum(bseq),rcsg|]}||gqSrr)rr)r+rrrsz&havel_hakimi_graph..csg|]}||gqSrr)rr)r.naseqrrrsNr Zbipartite_havel_hakimi_graph)rrr2rrr3r4r5r6r8sortpopadd_edgeremover) r+r.r&r'nbseqr<r=r0r1degreertargetrr)r+r.r?rrs:     c sLtjd|tjd}|jr$tjdtt}t}t}||ksbtjd|d|t||}tdkstdkr|Sfddt dD}fddt |D}|j |j xp|r@|j \} } | dkrPxN|d| D]>} | d } |j | | | dd 8<| ddkr|j | qWqWd |_|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 r)r*zDirected Graph not supportedz/invalid degree sequences, sum(aseq)!=sum(bseq),rcsg|]}||gqSrr)rr)r+rrr sz.reverse_havel_hakimi_graph..csg|]}||gqSrr)rr)r.r/rrr sr Z$bipartite_reverse_havel_hakimi_graph)rrr2rrr3r4r5r6r8r@rArBrCr) r+r.r&r'r;r<r=r0r1rErrFrr)r+r.r/rrs:      cstjd|tjd}|jr$tjdtt}t}t}||ksbtjd|d|t||}tdkstdkr|Sfddt dD}fddt |D}x|r|j |j \} } | dkrP|j |d| d } || | d d } d dt | | D} t| t| t| krP| j | j xJ| D]B}|d }|j| ||dd 8<|ddkrV|j|qVWqWd |_|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 r)r*zDirected Graph not supportedz/invalid degree sequences, sum(aseq)!=sum(bseq),rcsg|]}||gqSrr)rr)r+rrrSsz2alternating_havel_hakimi_graph..csg|]}||gqSrr)rr)r.r?rrrTsNcSsg|]}|D]}|q qSrr)rzr-rrrr]sr Z(bipartite_alternating_havel_hakimi_graph)rrr2rrr3r4r5r6r8r@rAzipappendrBrCr)r+r.r&r'rDr<r=r0r1rErsmallZlarger>rFrr)r+r.r?rrsD!     c sBtjd|tjdjr$tjd|dkr>tjd|dt}t|dfddtd|D}x|r6x|dr$|dd}|dj||j |kst|krt}j |dd j ||qtfd dt|tD}t d d |} |j | }j |dd j ||qtW|j|dqlWd _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 r)r*zDirected Graph not supportedr z probability z > 1csg|]}|g|qSrr)rr)r+rrrsz1preferential_attachment_graph..)rcsg|]}|gj|qSr)rE)rb)r'rrrscSs||S)Nr)r-yrrrsz/preferential_attachment_graph..Z'bipartite_preferential_attachment_model)rrr2rrr3r5r8rCrandomadd_noderBrchoicer) r+pr&r:r?vvsourcerFZbbZbbstubsr)r'r+rr ks0(     Fc Csptj}t|||}|r"tj|}d|d|d|d|_|dkrH|S|dkr\tj||Stjd|}d}d}xp||krtjd|j} |dt | |}x$||kr||kr||}|d}qW||krt|j |||qtW|rld}d}xx||krjtjd|j} |dt | |}x*||krN||krN||}|d}q&W||kr|j |||qW|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(rrrr g?rU) rGraphr5DiGraphrr mathlogrOintrB) nmrRr:directedr'Zlprwlrrrrr s@-      c Cstj}t|||}|r"tj|}d|d|d|d|_|dksL|dkrP|S||}||krptj|||dSdd|jdd D}tt|t|}d } xD| |kr|j |} |j |} | || krqq|j | | | d7} qW|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(rrr )r&cSs g|]\}}|ddkr|qS)rrr)rr[drrrr?sz%gnmk_random_graph..T)datar) rrVr5rWrr ZnodeslistsetrQrB) r[r\kr:r]r'Z max_edgesr(rZ edge_countrrrrrr s*,        cCsd|jtd||tttd|dg|}|jttt|||dg|tj||d|S)Nrr r)r#r8dictrIupdaterZset_node_attributes)r'r/r;rLrrrr5Ns $r5)N)NN)N)N)N)NN)NF)NF)__doc__rXr! functoolsrZnetworkxrZnetworkx.utilsrr__all__r rrrrr r r r5rrrrs6   ) J J I M F U E