ó |£*^c@s™dZddlZddlmZddlmZdZdddd d d d d ddddddddddddgZddlZ ddlm Z m Z d„Z dd„Zdd„Zdd„Zdd„Zdd „Zdd!„Zdd"„Zdd#„Zd$dd%„Zedd&„Zed'„Zd(„Zdd)„Zdd*„Zdd+„Zdd,„Zdd-„Zdd.„Z dd/„Z!d0„Z"dS(1s5 Generators for some classic graphs. The typical graph generator is called as follows: >>> G=nx.complete_graph(100) returning the complete graph on n nodes labeled 0,..,99 as a simple graph. Except for empty_graph, all the generators in this module return a Graph class (i.e. a simple, undirected graph). iÿÿÿÿN(tcomplete_bipartite_graph(t accumulates=Aric Hagberg (hagberg@lanl.gov) Pieter Swart (swart@lanl.gov)t balanced_treet barbell_graphtcomplete_graphtcomplete_multipartite_graphtcircular_ladder_graphtcirculant_grapht cycle_grapht dorogovtsev_goltsev_mendes_grapht empty_graphtfull_rary_treet grid_grapht grid_2d_graphthypercube_grapht ladder_graphtlollipop_grapht null_grapht path_grapht star_grapht trivial_grapht wheel_graph(tis_list_of_intstflattenccs•tt|ƒƒ}t|ƒg}xm|r|jdƒ}xQt|ƒD]C}y(t|ƒ}|j|ƒ||fVWqFtk rˆPqFXqFWq$WdS(Ni(titertrangetnexttpoptappendt StopIteration(tntrtnodestparentstsourcetittarget((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pyt _tree_edges6s    cCs,tj||ƒ}|jt||ƒƒ|S(sACreates a full r-ary tree of n vertices. Sometimes called a k-ary, n-ary, or m-ary tree. "... all non-leaf vertices have exactly r children and all levels are full except for some rightmost position of the bottom level (if a leaf at the bottom level is missing, then so are all of the leaves to its right." [1]_ Parameters ---------- r : int branching factor of the tree n : int Number of nodes in the tree create_using : NetworkX graph type, optional Use specified type to construct graph (default = networkx.Graph) Returns ------- G : networkx Graph An r-ary tree with n nodes References ---------- .. [1] An introduction to data structures and algorithms, James Andrew Storer, Birkhauser Boston 2001, (page 225). (tnxR tadd_edges_fromR%(RRt create_usingtG((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pyR EscCst|dkrd}n td||dd|ƒ}tj||ƒ}|jt||ƒƒ|Stj|||ƒS(sœReturn the perfectly balanced r-tree of height h. Parameters ---------- r : int Branching factor of the tree h : int Height of the tree create_using : NetworkX graph type, optional Use specified type to construct graph (default = networkx.Graph) Returns ------- G : networkx Graph A tree with n nodes Notes ----- This is the rooted tree where all leaves are at distance h from the root. The root has degree r and all other internal nodes have degree r+1. Node labels are the integers 0 (the root) up to number_of_nodes - 1. Also refered to as a complete r-ary tree. ii(tintR&R R'R%R (RthR(RR)((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pyRes   cs{|d k r*|jƒr*tjdƒ‚nˆdkrHtjdƒ‚nˆdkrftjdƒ‚ntˆ|ƒ}dˆˆf|_|jgtˆˆˆdƒD] }|^q¦ƒˆdkr|jgtˆˆˆdƒD]}||df^qãƒn|j‡‡fd†tˆˆdˆˆƒDƒƒ|j ˆdˆƒˆdkrw|j ˆˆdˆˆƒn|S( syReturn the Barbell Graph: two complete graphs connected by a path. For m1 > 1 and m2 >= 0. Two identical complete graphs K_{m1} form the left and right bells, and are connected by a path P_{m2}. The 2*m1+m2 nodes are numbered 0,...,m1-1 for the left barbell, m1,...,m1+m2-1 for the path, and m1+m2,...,2*m1+m2-1 for the right barbell. The 3 subgraphs are joined via the edges (m1-1,m1) and (m1+m2-1,m1+m2). If m2=0, this is merely two complete graphs joined together. This graph is an extremal example in David Aldous and Jim Fill's etext on Random Walks on Graphs. sDirected Graph not supportedis+Invalid graph description, m1 should be >=2is+Invalid graph description, m2 should be >=0sbarbell_graph(%d,%d)ic3s=|]3}t|ddˆˆƒD]}||fVq"qdS(iiN(R(t.0tutv(tm1tm2(so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pys ±sN( tNonet is_directedR&t NetworkXErrorRtnametadd_nodes_fromRR'tadd_edge(R/R0R(R)R.((R/R0so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pyR‹s$    1 >5 cCs{t||ƒ}d||_|dkrw|jƒrOtjt|ƒdƒ}ntjt|ƒdƒ}|j|ƒn|S(s] Return the complete graph K_n with n nodes. Node labels are the integers 0 to n-1. scomplete_graph(%d)ii(R R4R2t itertoolst permutationsRt combinationsR'(RR(R)tedges((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pyR¸s   cCsLt||ƒ}d||_|jd|dƒ|j|d|dƒ|S(sÝReturn the circular ladder graph CL_n of length n. CL_n consists of two concentric n-cycles in which each of the n pairs of concentric nodes are joined by an edge. Node labels are the integers 0 to n-1 scircular_ladder_graph(%d)iii(RR4R6(RR(R)((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pyRÈs  cCs—t||ƒ}d}||djd„|Dƒƒf|_xUt|ƒD]G}x>|D]6}|j||||ƒ|j||||ƒqUWqHW|S(sGenerates the circulant graph Ci_n(x_1, x_2, ..., x_m) with n vertices. Returns ------- The graph Ci_n(x_1, ..., x_m) consisting of n vertices 0, ..., n-1 such that the vertex with label i is connected to the vertices labelled (i + x) and (i - x), for all x in x_1 up to x_m, with the indices taken modulo n. Parameters ---------- n : integer The number of vertices the generated graph is to contain. offsets : list of integers A list of vertex offsets, x_1 up to x_m, as described above. create_using : NetworkX graph type, optional Use specified type to construct graph (default = networkx.Graph) Examples -------- Many well-known graph families are subfamilies of the circulant graphs; for example, to generate the cycle graph on n points, we connect every vertex to every other at offset plus or minus one. For n = 10, >>> import networkx >>> G = networkx.generators.classic.circulant_graph(10, [1]) >>> edges = [ ... (0, 9), (0, 1), (1, 2), (2, 3), (3, 4), ... (4, 5), (5, 6), (6, 7), (7, 8), (8, 9)] ... >>> sorted(edges) == sorted(G.edges()) True Similarly, we can generate the complete graph on 5 points with the set of offsets [1, 2]: >>> G = networkx.generators.classic.circulant_graph(5, [1, 2]) >>> edges = [ ... (0, 1), (0, 2), (0, 3), (0, 4), (1, 2), ... (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)] ... >>> sorted(edges) == sorted(G.edges()) True scirculant_graph(%d, [%s])s, css|]}t|ƒVqdS(N(tstr(R,tj((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pys s(R tjoinR4RR6(RtoffsetsR(R)ttemplateR#R<((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pyRØs-&  cCsCt||ƒ}d||_|dkr?|j|ddƒn|S(sÖReturn the cycle graph C_n over n nodes. C_n is the n-path with two end-nodes connected. Node labels are the integers 0 to n-1 If create_using is a DiGraph, the direction is in increasing order. scycle_graph(%d)ii(RR4R6(RR(R)((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pyRs   cCs|dk rK|jƒr*tjdƒ‚n|jƒrKtjdƒ‚qKntd|ƒ}d|_|jddƒ|dkrƒ|Sd}x‡td|dƒD]r}|j ƒ}t |ƒ}xQtd|ƒD]@}|j|||dƒ|j|||dƒ|d7}qËWqW|S(s¬Return the hierarchically constructed Dorogovtsev-Goltsev-Mendes graph. n is the generation. See: arXiv:/cond-mat/0112143 by Dorogovtsev, Goltsev and Mendes. sDirected Graph not supportedsMultigraph not supportedis Dorogovtsev-Goltsev-Mendes GraphiiN( R1R2R&R3t is_multigraphR R4R6RR:tlen(RR(R)tnew_nodeR#tlast_generation_edgest"number_of_edges_in_last_generationR<((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pyR s&       icCsO|dkrtjƒ}n|}|jƒ|jt|ƒƒd||_|S(sóReturn the empty graph with n nodes and zero edges. Node labels are the integers 0 to n-1 For example: >>> G=nx.empty_graph(10) >>> G.number_of_nodes() 10 >>> G.number_of_edges() 0 The variable create_using should point to a "graph"-like object that will be cleaned (nodes and edges will be removed) and refitted as an empty "graph" with n nodes with integer labels. This capability is useful for specifying the class-nature of the resulting empty "graph" (i.e. Graph, DiGraph, MyWeirdGraphClass, etc.). The variable create_using has two main uses: Firstly, the variable create_using can be used to create an empty digraph, network,etc. For example, >>> n=10 >>> G=nx.empty_graph(n,create_using=nx.DiGraph()) will create an empty digraph on n nodes. Secondly, one can pass an existing graph (digraph, pseudograph, etc.) via create_using. For example, if G is an existing graph (resp. digraph, pseudograph, etc.), then empty_graph(n,create_using=G) will empty G (i.e. delete all nodes and edges using G.clear() in base) and then add n nodes and zero edges, and return the modified graph (resp. digraph, pseudograph, etc.). See also create_empty_copy(G). sempty_graph(%d)N(R1R&tGraphtclearR5RR4(RR(R)((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pyR 7s%   cs¦td|ƒ}d|_tˆƒ}tˆƒ‰|j‡fd†|Dƒƒ|j‡fd†|Dƒƒ|j‡fd†|Dƒƒ|jƒrÖ|j‡‡fd†|Dƒƒ|j‡‡fd†|Dƒƒn|r¢ˆdkr4|j‡fd †|Dƒƒ|jƒr4|j‡fd †|Dƒƒq4nˆdkrŒ|j‡fd †ˆDƒƒ|jƒrŒ|j‡fd †ˆDƒƒqŒnd ˆˆf|_n|S(sË Return the 2d grid graph of mxn nodes, each connected to its nearest neighbors. Optional argument periodic=True will connect boundary nodes via periodic boundary conditions. iR c3s(|]}ˆD]}||fVq qdS(N((R,R#R<(tcolumns(so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pys qsc3sD|]:}ˆD]-}|dkr ||f|d|ffVq qdS(iiN((R,R#R<(RG(so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pys rsc3sD|]:}ˆD]-}|dkr ||f||dffVq qdS(iiN((R,R#R<(RG(so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pys ssc3sH|]>}ˆD]1}|ˆdkr ||f|d|ffVq qdS(iN((R,R#R<(RGtm(so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pys usc3sH|]>}ˆD]1}|ˆdkr ||f||dffVq qdS(iN((R,R#R<(RGR(so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pys vsic3s+|]!}|df|ˆdffVqdS(iiN((R,R#(R(so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pys ysc3s+|]!}|ˆdf|dffVqdS(iiN((R,R#(R(so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pys {sc3s+|]!}d|fˆd|ffVqdS(iiN((R,R<(RH(so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pys }sc3s+|]!}ˆd|fd|ffVqdS(iiN((R,R<(RH(so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pys ssperiodic_grid_2d_graph(%d,%d)(R R4RR5R'R2(RHRtperiodicR(R)trows((RGRHRso/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pyR gs*     #  #  #c Cs d|}|gkr3tdƒ}d||_|St|ƒsQtjdƒ‚nt|ƒdkrutjdƒ‚n|r„t}nt}t|ƒ}|j ƒ}||ƒ}xLt |ƒdkrü|j ƒ}|j ƒ}||ƒ}tj ||ƒ}q±Wtj |tƒ}d||_|S(s. Return the n-dimensional grid graph. The dimension is the length of the list 'dim' and the size in each dimension is the value of the list element. E.g. G=grid_graph(dim=[2,3]) produces a 2x3 grid graph. If periodic=True then join grid edges with periodic boundary conditions. s%sisgrid_graph(%s)sdim is not a list of integerss/dim is not a list of strictly positive integers(R R4RR&R3tminRRtlistRRAtcopytcartesian_productt relabel_nodesR( tdimRItdlabelR)tfunct current_dimtGoldtGnewtH((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pyR „s0              cCs*|dg}t|ƒ}d||_|S(sZReturn the n-dimensional hypercube. Node labels are the integers 0 to 2**n - 1. ishypercube_graph_(%d)(R R4(RRPR)((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pyR¯s   cCsí|dk r*|jƒr*tjdƒ‚ntd||ƒ}d||_|jgt|dƒD]}||df^qaƒ|jgt|d|dƒD]}||df^qœƒ|jgt|ƒD]}|||f^q̃|S(s«Return the Ladder graph of length n. This is two rows of n nodes, with each pair connected by a single edge. Node labels are the integers 0 to 2*n - 1. sDirected Graph not supportedisladder_graph_(%d)iN(R1R2R&R3R R4R'R(RR(R)R.((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pyRºs  4;0cCs&|dk r*|jƒr*tjdƒ‚n|dkrHtjdƒ‚n|dkrftjdƒ‚nt||ƒ}|jgt|||ƒD] }|^qƒ|dkrì|jgt|||dƒD]}||df^q̃n|dkr|j|d|ƒnd||f|_ |S( s9Return the Lollipop Graph; `K_m` connected to `P_n`. This is the Barbell Graph without the right barbell. For m>1 and n>=0, the complete graph K_m is connected to the path P_n. The resulting m+n nodes are labelled 0,...,m-1 for the complete graph and m,...,m+n-1 for the path. The 2 subgraphs are joined via the edge (m-1,m). If n=0, this is merely a complete graph. Node labels are the integers 0 to number_of_nodes - 1. (This graph is an extremal example in David Aldous and Jim Fill's etext on Random Walks on Graphs.) sDirected Graph not supportedis*Invalid graph description, m should be >=2is*Invalid graph description, n should be >=0islollipop_graph(%d,%d)N( R1R2R&R3RR5RR'R6R4(RHRR(R)R.((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pyRÌs     - > cCstd|ƒ}d|_|S(seReturn the Null graph with no nodes or edges. See empty_graph for the use of create_using. is null_graph()(R R4(R(R)((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pyRñs cCsTt||ƒ}d||_|jgt|dƒD]}||df^q3ƒ|S(sÏReturn the Path graph P_n of n nodes linearly connected by n-1 edges. Node labels are the integers 0 to n - 1. If create_using is a DiGraph then the edges are directed in increasing order. spath_graph(%d)i(R R4R'R(RR(R)R.((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pyRûs 4cCs#td||ƒ}d||_|S(s‚ Return the Star graph with n+1 nodes: one center node, connected to n outer nodes. Node labels are the integers 0 to n. isstar_graph(%d)(RR4(RR(R)((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pyRs cCstd|ƒ}d|_|S(sR Return the Trivial graph with one node (with integer label 0) and no edges. istrivial_graph()(R R4(R(R)((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pyRs cCs|dkrtj|d|ƒSt|d|ƒ}d||_|jgtd|dƒD]}||df^qYƒ|dkr™|jd|dƒn|S(s“ Return the wheel graph: a single hub node connected to each node of the (n-1)-node cycle graph. Node labels are the integers 0 to n - 1. iR(iswheel_graph(%d)i(R&R RR4R'RR6(RR(R)R.((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pyRs  7 c Gsçtjt|ƒƒ}tdgtt|ƒƒt|ƒƒ}g|D]\}}t||ƒ^qD}x-t|ƒD]\}}|j|d|ƒqrWx9t j |dƒD]%\}} |j t j || ƒƒq¨Wdj |ƒ|_|S(sReturns the complete multipartite graph with the specified block sizes. Parameters ---------- block_sizes : tuple of integers The number of vertices in each block of the multipartite graph. The length of this tuple is the number of blocks. Returns ------- G : NetworkX Graph Returns the complete multipartite graph with the specified block sizes. For each node, the node attribute ``'block'`` is an integer indicating which block contains the node. Examples -------- Creating a complete tripartite graph, with blocks of one, two, and three vertices, respectively. >>> import networkx as nx >>> G = nx.complete_multipartite_graph(1, 2, 3) >>> [G.node[u]['block'] for u in G] [0, 1, 1, 2, 2, 2] >>> G.edges(0) [(0, 1), (0, 2), (0, 3), (0, 4), (0, 5)] >>> G.edges(2) [(2, 0), (2, 3), (2, 4), (2, 5)] >>> G.edges(4) [(4, 0), (4, 1), (4, 2)] Notes ----- This function generalizes several other graph generator functions. - If no block sizes are given, this returns the null graph. - If a single block size ``n`` is given, this returns the empty graph on ``n`` nodes. - If two block sizes ``m`` and ``n`` are given, this returns the complete bipartite graph on ``m + n`` nodes. - If block sizes ``1`` and ``n`` are given, this returns the star graph on ``n + 1`` nodes. See also -------- complete_bipartite_graph itblockiscomplete_multiparite_graph{0}(R&R tsumtzipRLRRt enumerateR5R7R9R'tproducttformatR4( t block_sizesR)textentststarttendtblocksR#RWtblock1tblock2((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pyR*s9(((#t__doc__R7t(networkx.algorithms.bipartite.generatorsRtnetworkx.utilsRt __author__t__all__tnetworkxR&RRR%R1R RRRRRRR R tFalseR R RRRRRRRRR(((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/classic.pyt s^     & -   6  0 +  %