ܛ7i/dZddlZddlmZddlmZddlZgdZdZ ejjdejjdejd dd Zejjdejjd dZejjd dd ddZy)zOFunctions for splitting a network into two communities (finding a bipartition).N)deepcopy)count)kernighan_lin_bisectionspectral_modularity_bipartitiongreedy_node_swap_bipartitionc#$ Ktjjtjjfx\}} jD]R\}}t fd|jD}|r|j ||@|j || T fd}d}d} |rV|rS|j \}}|||j \} } || | || zz } |dz }| ||| ff|r|rQyyyyw)z This is a modified form of Kernighan-Lin, which moves single nodes at a time, alternating between sides to keep the bisection balanced. We keep two min-heaps of swap costs to make optimal-next-move selection fast. c38K|]\}}|r|n| ywN).0vwtsides g/home/rose/Desktop/poly/venv/lib/python3.12/site-packages/networkx/algorithms/community/bipartitions.py z'_kernighan_lin_sweep..s#F247R+sc |}|jD]G\}} |}||k(r| }|}||vs|j|d|zz}|j||dIy)NT)allow_increase)itemsgetinsert) node side_nodenbrrside_nbrheap_nbrcost_nbr cost_heaps edge_infors r_update_heap_valuesz1_kernighan_lin_sweep.._update_heap_valuessyJ  ,,.GCCyH9$S!(+Hh#<<,q2v5XdC/rN)nxutils BinaryHeaprsumrpop) rrheap0heap1unbrscost_ur itotcostr cost_vrs `` @r_kernighan_lin_sweepr0s !# 3 3 5rxx7J7J7L LLLE5:??$4FFF 7 LLF # LLVG $ % D AG EIIK 6AIIK 6A6F?" Qq1a&   E%E%s DD Ddirectedweight) edge_attrs ct|}|*|j|t|dz}|d|||d}}n= |\}}t jj|||gst j d|D cic]} | | |v } } tr} n|jrfd} nfd} |jjD cic]7\} }| |jDcic]\}}| | ||x}||c}}9}}}} }t|D]H}tt|| }t|\}}}|dk\rn|d|D]\}}\} }d| | <d| |<J| jD chc] \} }|dk(s | }} }| jD chc] \} }|dk(s | }} }||fS#ttf$r} t j d| d} ~ wwxYwcc} wcc}}wcc}}}} wcc}} wcc}} w) u Partition a graph into two blocks using the Kernighan–Lin algorithm. This algorithm partitions a network into two sets by iteratively swapping pairs of nodes to reduce the edge cut between the two sets. The pairs are chosen according to a modified form of Kernighan-Lin [1]_, which moves nodes individually, alternating between sides to keep the bisection balanced. Kernighan-Lin is an approximate algorithm for maximal modularity bisection. In [2]_ they suggest that fine-tuned improvements can be made using greedy node swapping, (see `greedy_node_swap_bipartition`). The improvements are typically only a few percent of the modularity value. But they claim that can make a difference between a good and excellent method. This function does not perform any improvements. But you can do that yourself. Parameters ---------- G : NetworkX graph Graph must be undirected. partition : tuple Pair of iterables containing an initial partition. If not specified, a random balanced partition is used. max_iter : int Maximum number of times to attempt swaps to find an improvement before giving up. weight : string or function (default: "weight") If this is a string, then edge weights will be accessed via the edge attribute with this key (that is, the weight of the edge joining `u` to `v` will be ``G.edges[u, v][weight]``). If no such edge attribute exists, the weight of the edge is assumed to be one. If this is a function, the weight of an edge is the value returned by the function. The function must accept exactly three positional arguments: the two endpoints of an edge and the dictionary of edge attributes for that edge. The function must return a number or None to indicate a hidden edge. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. Only used if partition is None Returns ------- partition : tuple A pair of sets of nodes representing the bipartition. Raises ------ NetworkXError If `partition` is not a valid partition of the nodes of the graph. References ---------- .. [1] Kernighan, B. W.; Lin, Shen (1970). "An efficient heuristic procedure for partitioning graphs." *Bell Systems Technical Journal* 49: 291--307. Oxford University Press 2011. .. [2] M. E. J. Newman, "Modularity and community structure in networks", PNAS, 103 (23), p. 8577-8582, https://doi.org/10.1073/pnas.0601602103 Nrzpartition must be two setszpartition invalidcHtfd|jDS)Nc3BK|]}|jdyw)r"Nr)r ddr3s rrz...s(PZr):Zs)r&valuesr*r dr3s rz)kernighan_lin_bisection..sS(PQXXZ(P%Pr!c(|jdS)Nr"r9r<s rr>z)kernighan_lin_bisection..sQUU61%5r!rr")listshufflelen TypeError ValueErrorr# NetworkXError community is_partitioncallable is_multigraph_adjrranger0min)G partitionmax_iterr3seednodesmidABerrrr sum_weightr*r+r r=rrr-costsmin_costmin_i_spart1part2s ` rrr7s$P GE U%jAoTc{E#$K1 JDAq||((QF3""#67 7*/ 0%$D419 %D 0  P 5 vv||~%GAt djjl VldaZ1a5H/Hr.UArEl VV% 8_))T:; Z% q= !&5MLAq&1aDGDG* ::< 2<41a16Q>> G = nx.karate_club_graph() >>> MrHi, Officer = nx.community.spectral_modularity_bipartition(G) >>> MrHi, Officer = sorted([sorted(MrHi), sorted(Officer)]) >>> MrHi [0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 16, 17, 19, 21] >>> Officer [8, 9, 14, 15, 18, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33] References ---------- .. [1] M. E. J. Newman *Networks: An Introduction*, pages 373--378 Oxford University Press 2011. .. [2] M. E. J. Newman, "Modularity and community structure in networks", PNAS, 103 (23), p. 8577-8582, https://doi.org/10.1073/pnas.0601602103 rN) numpyr#linalgmodularity_matrixeigargsortziprealsetadd) rMnprT eigenvalues eigenvectorsindexv2leftrightr*ns rrrsd ##A&A " a 0K JJ{ #B 'E RWW\!U(+ ,a 0B%%D1 q5 HHQK IIaL  ;r!) init_splitrOc"|]t|dz}t||z }ttjt ||}|Dchc] }||vs| }}||f}nct j j||st jdt|dk(st jdt|}t j j||} || } } d} |j} t|j"| | k\rG| |krA| }| } t| }| }t|}|rd}d}d}|\}}t"fd|D}t"fd|D}|D]}||vr ||}}||}}n||}}||}}t||j|z | z }t||j|z| z }"|}|d| dzzz ||z |z z}||z|z} | |kDs| }|}|}|}!|j!|!j#|||z }|| kDr t||} } |j!||r| d z } | | k\r| |krA|Scc}w) aaSplit the nodes into two communities based on greedy modularity maximization. The algorithm works by selecting a node to change communities which will maximize the modularity. The swap is made and the community structure with the highest modularity is kept. Parameters ---------- G : NetworkX graph init_split : 2-tuple of sets of nodes Pair of sets of nodes in ``G`` providing an initial bipartition for the algorithm. If not specified, a random balanced partition is used. If this pair of sets is not a partition of the nodes of `G`, :exc:`NetworkXException` is raised. max_iter : int Maximum number of iterations of attempting swaps to find an improvement. Returns ------- max_split : 2-tuple of sets of nodes Pair of sets of nodes of ``G``, partitioned according to a node swap greedy modularity maximization algorithm. Raises ------ NetworkXError if init_split is not a valid partition of the graph into two communities or if G is a MultiGraph Examples -------- >>> G = nx.barbell_graph(3, 0) >>> left, right = nx.community.greedy_node_swap_bipartition(G) >>> # Sort the communities so the nodes appear in increasing order. >>> left, right = sorted([sorted(left), sorted(right)]) >>> sorted(left) [0, 1, 2] >>> sorted(right) [3, 4, 5] Notes ----- This function is not implemented for multigraphs. References ---------- .. [1] M. E. J. Newman "Networks: An Introduction", pages 373--375. Oxford University Press 2011. Nrz"init_split is not a partition of Gz init_split must be a bipartitionrr`c3(K|] }| ywr r r rqG_degrees rrz/greedy_node_swap_bipartition..Ds2T Tc3(K|] }| ywr r rus rrz/greedy_node_swap_bipartition..Es4e!erwr")rBrhrandomsampler@r#rFrGrEr modularitynumber_of_edgesdictdegreer&keysremoveri)#rMrrrOm1m2 some_nodesrq other_nodesbest_split_so_farbest_mod max_splitmax_moditsm next_splitnext_modrQmax_swapmax_node max_node_commrorpleftdrightdin_commout_commin_degout_degd_eiid_ejjdegd_sum_ai swap_changenon_max_node_commrvs# @rrrsn Vq[ Vb[tAw34 "#;!Qq ':q! ;'5||((J7""#GH H:!#""#EF F$Z0||&&q*;rsU  $!Nj)!X&p'*pfj)l+<,*<~l+26s,sr!