ިsgFdZddlmZddlZddlmZddlmZddl m Z ddgZ dd Z ejd  dd Zed edejd ddZy)z8Functions for detecting communities based on modularity.) defaultdictN) modularity)not_implemented_for) MappedQueuegreedy_modularity_communities#naive_greedy_modularity_communitiesc#x K|j}|j}|j|}d|z }|rQ|j|Dcic] \}}|||z } }}|j |D cic] \}} || |z } }} n.|j |D cic]\}} || |zdzc} }x} } t d} |j|dD],\}}}||k(r | ||xx|z cc<| ||xx|z cc<.| jD]C\}}|jD]+\}}||z|| || |z| || |zzzz | ||<-E|Dcic]6}|t| |jDcic] \}}||f|  c}}8}}}}t|Dcgc]&}t||dkDs||jd(c}}|Dcic]}|t|g}}|jt|dkDrh |j\}}}| }|||jt||dkDr!|j!||jd||jd||fk(r\|j#||f||j#||ft||dkDr8|j!||jdn||j#||ft||||z||<||=t%| |}t%| |}||z||hz }||z}|D]*}||vr| ||| ||z}nK||vr$| |||| || |z| || |zzzz }n#| |||| || |z| || |zzzz }||f||ffD]\}}||} || ||<t| dkDr| jd}!nd}!||f}"| }#||vr| j'|"|"|#n| j!|"|#|!|j!|"|#|| jd}$|!|$k7s|!j(|$j(k7s|j'|!|$-| |D]}| ||}%| ||=||k7s||f||ffD]\}}||} ||f}&| jd|&k(rP| j#|&|j#|&t| dkDsR|j!| jdq| j#|&| |=t||<| |xx| |z cc<d| |<|r| |xx| |z cc<d| |<|jt|dkDrgyycc}}wcc} }wcc} }wcc}}wcc}}}wcc}wcc}w#t$rYywxYww) aYield community partitions of G and the modularity change at each step. This function performs Clauset-Newman-Moore greedy modularity maximization [2]_ At each step of the process it yields the change in modularity that will occur in the next step followed by yielding the new community partition after that step. Greedy modularity maximization begins with each node in its own community and repeatedly joins the pair of communities that lead to the largest modularity until one community contains all nodes (the partition has one set). This function maximizes the generalized modularity, where `resolution` is the resolution parameter, often expressed as $\gamma$. See :func:`~networkx.algorithms.community.quality.modularity`. Parameters ---------- G : NetworkX graph weight : string or None, optional (default=None) The name of an edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1. The degree is the sum of the edge weights adjacent to the node. resolution : float (default=1) If resolution is less than 1, modularity favors larger communities. Greater than 1 favors smaller communities. Yields ------ Alternating yield statements produce the following two objects: communities: dict_values A dict_values of frozensets of nodes, one for each community. This represents a partition of the nodes of the graph into communities. The first yield is the partition with each node in its own community. dq: float The change in modularity when merging the next two communities that leads to the largest modularity. See Also -------- modularity References ---------- .. [1] Newman, M. E. J. "Networks: An Introduction", page 224 Oxford University Press 2011. .. [2] Clauset, A., Newman, M. E., & Moore, C. "Finding community structure in very large networks." Physical Review E 70(6), 2004. .. [3] Reichardt and Bornholdt "Statistical Mechanics of Community Detection" Phys. Rev. E74, 2006. .. [4] Newman, M. E. J."Analysis of weighted networks" Physical Review E 70(5 Pt 2):056131, 2004. )weightg?c ttS)N)rfloat_/var/www/html/venv/lib/python3.12/site-packages/networkx/algorithms/community/modularity_max.pyz:_greedy_modularity_communities_generator..[s +e"4r)datadefaultrN)priority) is_directednumber_of_nodessize out_degree in_degreedegreeredgesitemsrlenheap frozensetvaluespop IndexErrorpushremovesetupdater)'Gr resolutiondirectedNmq0nodedeg_outadeg_inbdegdq_dictuvwtnbrdictdqdq_heapnH communitiesnegdqu_nbrsv_nbrsall_nbrs both_nbrswdq_vwrowcol dq_heap_rowd_oldmaxdd_negdqrow_maxdq_oldd_olds' r(_greedy_modularity_communities_generatorrMslr}}H A vA QB 56\\\5P QMD'T7R<  Q Q34;;f;3M N<4T6B;  N N78xxvx7NO)$sRx#~%OOA45GGGG31b 6  1   1  mmoO 7]]_ OEArGjAaD1Q4K!A$1+4M&NNGAJqM OO WXXXQRq+ 8H8H8JKuq"1vs{KLLXGXJAc'!*o6IWQZ__Q'JKA/001in$0K0     a&1* %%'KE1aV  wqz?Q  FF71:??1% & 1:??1 !Q ' HHaV  AJ  q!f %71:"wqzq)* AJ  q!f %#;q>KN#BC A NWQZWQZVO1v-VO $ 4AI~ 1  1 5f 1 adQqTkAaD1Q4K6O(PP 1 adQqTkAaD1Q4K6O(PPVaV, 4S%cl $) S!{#a'*//2H#H#J &;&&q!g&> $$Q$9#FF1wF/*..q1G7*h.?.?7CSCS.S737 4$ 4N 2AQZ]F 1 Av"#Q!Q 0 2HC")#,K #JE"''*e3#**51{+a/FF;#3#3A#67$**51 2 2, AJ ]  !! !  aDAaDLDAaD  ""[ a&1*= R NO$LXJ1   sAV:V V:8VV:!V4B0V:$!VV V V:,V!V! V:"V&6#V:V+.H2V:!2V:AV:.BV:V:VV:+ V74V:6V77V:r ) edge_attrsc*|js|Dcgc]}|hc}S|dks||jkDrtdt|d|d|Z|dks||jkDrtdt|d|d||krtd|d||dk(rt |gS|j}t |||}t |}t||kDr: t |}|d krt||krnt |}t||kDr:t|td Scc}w#t$rPt|td }t||kDr+|^} } } | | z g}|j| t||kDr+|cYSwxYw) a, Find communities in G using greedy modularity maximization. This function uses Clauset-Newman-Moore greedy modularity maximization [2]_ to find the community partition with the largest modularity. Greedy modularity maximization begins with each node in its own community and repeatedly joins the pair of communities that lead to the largest modularity until no further increase in modularity is possible (a maximum). Two keyword arguments adjust the stopping condition. `cutoff` is a lower limit on the number of communities so you can stop the process before reaching a maximum (used to save computation time). `best_n` is an upper limit on the number of communities so you can make the process continue until at most n communities remain even if the maximum modularity occurs for more. To obtain exactly n communities, set both `cutoff` and `best_n` to n. This function maximizes the generalized modularity, where `resolution` is the resolution parameter, often expressed as $\gamma$. See :func:`~networkx.algorithms.community.quality.modularity`. Parameters ---------- G : NetworkX graph weight : string or None, optional (default=None) The name of an edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1. The degree is the sum of the edge weights adjacent to the node. resolution : float, optional (default=1) If resolution is less than 1, modularity favors larger communities. Greater than 1 favors smaller communities. cutoff : int, optional (default=1) A minimum number of communities below which the merging process stops. The process stops at this number of communities even if modularity is not maximized. The goal is to let the user stop the process early. The process stops before the cutoff if it finds a maximum of modularity. best_n : int or None, optional (default=None) A maximum number of communities above which the merging process will not stop. This forces community merging to continue after modularity starts to decrease until `best_n` communities remain. If ``None``, don't force it to continue beyond a maximum. Raises ------ ValueError : If the `cutoff` or `best_n` value is not in the range ``[1, G.number_of_nodes()]``, or if `best_n` < `cutoff`. Returns ------- communities: list A list of frozensets of nodes, one for each community. Sorted by length with largest communities first. Examples -------- >>> G = nx.karate_club_graph() >>> c = nx.community.greedy_modularity_communities(G) >>> sorted(c[0]) [8, 14, 15, 18, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33] See Also -------- modularity References ---------- .. [1] Newman, M. E. J. "Networks: An Introduction", page 224 Oxford University Press 2011. .. [2] Clauset, A., Newman, M. E., & Moore, C. "Finding community structure in very large networks." Physical Review E 70(6), 2004. .. [3] Reichardt and Bornholdt "Statistical Mechanics of Community Detection" Phys. Rev. E74, 2006. .. [4] Newman, M. E. J."Analysis of weighted networks" Physical Review E 70(5 Pt 2):056131, 2004. r zcutoff must be between 1 and z. Got .zbest_n must be between 1 and z Must have best_n >= cutoff. Got z < )r r(Tkeyreverser) rr ValueErrorrr%rMnext StopIterationsortedextend) r'r r(cutoffbest_nr: community_genr<r8comm1comm2rests rrrsl 668 !2!2!448QvhaPQQ  QJFQ%6%6%88>> G = nx.karate_club_graph() >>> c = nx.community.naive_greedy_modularity_communities(G) >>> sorted(c[0]) [8, 14, 15, 18, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33] See Also -------- greedy_modularity_communities modularity N)r(r rr c3>K|]}t|dkDs|yw)rN)r).0cs r z6naive_greedy_modularity_communities..s8SVaZ18sTrQ) nodesrrlist enumeraterminappendrW)r'r(r r4r<mergesold_modularitynew_modularitytrial_communitiesto_mergeijr5trial_modularityr8s rrresd,-7795a9aS>5K5 FN;:fUN  N^$C' -k* )DAq!+. )16SVq[CFaK'(1u!!$'0}!!$#-(Z$ $~5'.8)9$%q.>*I#J!c!Qi#hqk8A;2O&O)9$%q.>*I#J'(!!$'(!!$- ) )0   MM( #HAq"q>;q>qAUKN&r]KNI  N^$CL 8k8c4 PPY6sE&)Nr )Nr r N)r N)__doc__ collectionsrnetworkxnx%networkx.algorithms.community.qualityrnetworkx.utilsrnetworkx.utils.mapped_queuer__all__rM _dispatchablerrrrrr{s>#<.3$)  O#dX&   6'6DZ \"X&[Q'#![Qr