ó |£*^c@sdZddlZddlmZmZddlZddlmZddlZddl Z ddl m Z dj ddd d gƒZd d d ddddgZddd„Zddd„Zded„Zdd„Zdd„Zdd„Zddd„Zdefd„ƒYZdS(sJGenerate graphs with a given degree sequence or expected degree sequence. iÿÿÿÿN(t combinationst permutations(t itemgetter(trandom_weighted_samples s%Aric Hagberg sPieter Swart sNDan Schult Joel Miller sINathan Lemons Brian Cloteaux tconfiguration_modeltdirected_configuration_modeltexpected_degree_graphthavel_hakimi_graphtdirected_havel_hakimi_graphtdegree_sequence_treetrandom_degree_sequence_graphc Csat|ƒddks(tjdƒ‚n|dkrCtjƒ}n|jƒratjdƒ‚n|dk r}tj|ƒnt|ƒ}tj ||ƒ}|dks¹t |ƒdkr½|Sg}x6|D].}x%t ||ƒD]}|j |ƒqáWqÊWtj |ƒx2|r=|jƒ}|jƒ} |j|| ƒq Wd|jƒ|jƒf|_|S(sø Return a random graph with the given degree sequence. The configuration model generates a random pseudograph (graph with parallel edges and self loops) by randomly assigning edges to match the given degree sequence. Parameters ---------- deg_sequence : list of integers Each list entry corresponds to the degree of a node. create_using : graph, optional (default MultiGraph) Return graph of this type. The instance will be cleared. seed : hashable object, optional Seed for random number generator. Returns ------- G : MultiGraph A graph with the specified degree sequence. Nodes are labeled starting at 0 with an index corresponding to the position in deg_sequence. Raises ------ NetworkXError If the degree sequence does not have an even sum. See Also -------- is_valid_degree_sequence Notes ----- As described by Newman [1]_. A non-graphical degree sequence (not realizable by some simple graph) is allowed since this function returns graphs with self loops and parallel edges. An exception is raised if the degree sequence does not have an even sum. This configuration model construction process can lead to duplicate edges and loops. You can remove the self-loops and parallel edges (see below) which will likely result in a graph that doesn't have the exact degree sequence specified. The density of self-loops and parallel edges tends to decrease as the number of nodes increases. However, typically the number of self-loops will approach a Poisson distribution with a nonzero mean, and similarly for the number of parallel edges. Consider a node with k stubs. The probability of being joined to another stub of the same node is basically (k-1)/N where k is the degree and N is the number of nodes. So the probability of a self-loop scales like c/N for some constant c. As N grows, this means we expect c self-loops. Similarly for parallel edges. References ---------- .. [1] M.E.J. Newman, "The structure and function of complex networks", SIAM REVIEW 45-2, pp 167-256, 2003. Examples -------- >>> from networkx.utils import powerlaw_sequence >>> z=nx.utils.create_degree_sequence(100,powerlaw_sequence) >>> G=nx.configuration_model(z) To remove parallel edges: >>> G=nx.Graph(G) To remove self loops: >>> G.remove_edges_from(G.selfloop_edges()) iisInvalid degree sequencesDirected Graph not supporteds%configuration_model %d nodes %d edgesN(tsumtnxt NetworkXErrortNonet MultiGrapht is_directedtrandomtseedtlent empty_graphtmaxtrangetappendtshuffletpoptadd_edgetordertsizetname( t deg_sequencet create_usingRtNtGtstublisttntitn1tn2((sr/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/degree_seq.pyR"s.K         cCsît|ƒt|ƒks*tjdƒ‚n|dkrEtjƒ}n|dk ratj|ƒnt|ƒ}t|ƒ}||kr |j||dgƒn|j||dgƒt|ƒ}tj ||ƒ}|dksôt |ƒdkrø|Sg}x6|D].} x%t || ƒD]} |j | ƒqWqWg} x6|D].} x%t || ƒD]} | j | ƒq[WqDWtj |ƒtj | ƒx8|rÊ| rÊ| jƒ} |jƒ} |j| | ƒq“Wd|jƒ|jƒf|_|S(s Return a directed_random graph with the given degree sequences. The configuration model generates a random directed pseudograph (graph with parallel edges and self loops) by randomly assigning edges to match the given degree sequences. Parameters ---------- in_degree_sequence : list of integers Each list entry corresponds to the in-degree of a node. out_degree_sequence : list of integers Each list entry corresponds to the out-degree of a node. create_using : graph, optional (default MultiDiGraph) Return graph of this type. The instance will be cleared. seed : hashable object, optional Seed for random number generator. Returns ------- G : MultiDiGraph A graph with the specified degree sequences. Nodes are labeled starting at 0 with an index corresponding to the position in deg_sequence. Raises ------ NetworkXError If the degree sequences do not have the same sum. See Also -------- configuration_model Notes ----- Algorithm as described by Newman [1]_. A non-graphical degree sequence (not realizable by some simple graph) is allowed since this function returns graphs with self loops and parallel edges. An exception is raised if the degree sequences does not have the same sum. This configuration model construction process can lead to duplicate edges and loops. You can remove the self-loops and parallel edges (see below) which will likely result in a graph that doesn't have the exact degree sequence specified. This "finite-size effect" decreases as the size of the graph increases. References ---------- .. [1] Newman, M. E. J. and Strogatz, S. H. and Watts, D. J. Random graphs with arbitrary degree distributions and their applications Phys. Rev. E, 64, 026118 (2001) Examples -------- >>> D=nx.DiGraph([(0,1),(1,2),(2,3)]) # directed path graph >>> din=list(D.in_degree().values()) >>> dout=list(D.out_degree().values()) >>> din.append(1) >>> dout[0]=2 >>> D=nx.directed_configuration_model(din,dout) To remove parallel edges: >>> D=nx.DiGraph(D) To remove self loops: >>> D.remove_edges_from(D.selfloop_edges()) s9Invalid degree sequences. Sequences must have equal sums.is.directed configuration_model %d nodes %d edgesN(R R R Rt MultiDiGraphRRRtextendRRRRRRRRRR(tin_degree_sequencetout_degree_sequenceRRtnintnoutR R!t in_stublistR#R$t out_stublisttsourcettarget((sr/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/degree_seq.pyR•s>J            cCs,t|ƒ}tj|ƒ}|dks9t|ƒdkr=|S|dk rYtj|ƒndtt|ƒƒ}t t |ƒdt dƒdt ƒ}t d„t |ƒDƒƒ}g|D]\}} | ^q¶} |} |sç| d8} nx>t| ƒD]0}|} |s| d7} n| ||} | | | } | dkrDd} nxÝ| |kr#| dkr#| dkr­tjƒ}| ttjtj|ƒtjd| ƒƒƒ7} n| |krG| | | }|dkrÜd}ntjƒ|| kr |j|||| ƒn| d7} |} qGqGWqôW|S(saReturn a random graph with given expected degrees. Given a sequence of expected degrees `W=(w_0,w_1,\ldots,w_{n-1}`) of length `n` this algorithm assigns an edge between node `u` and node `v` with probability .. math:: p_{uv} = \frac{w_u w_v}{\sum_k w_k} . Parameters ---------- w : list The list of expected degrees. selfloops: bool (default=True) Set to False to remove the possibility of self-loop edges. seed : hashable object, optional The seed for the random number generator. Returns ------- Graph Examples -------- >>> z=[10 for i in range(100)] >>> G=nx.expected_degree_graph(z) Notes ----- The nodes have integer labels corresponding to index of expected degrees input sequence. The complexity of this algorithm is `\mathcal{O}(n+m)` where `n` is the number of nodes and `m` is the expected number of edges. The model in [1]_ includes the possibility of self-loop edges. Set selfloops=False to produce a graph without self loops. For finite graphs this model doesn't produce exactly the given expected degree sequence. Instead the expected degrees are as follows. For the case without self loops (selfloops=False), .. math:: E[deg(u)] = \sum_{v \ne u} p_{uv} = w_u \left( 1 - \frac{w_u}{\sum_k w_k} \right) . NetworkX uses the standard convention that a self-loop edge counts 2 in the degree of a node, so with self loops (selfloops=True), .. math:: E[deg(u)] = \sum_{v \ne u} p_{uv} + 2 p_{uu} = w_u \left( 1 + \frac{w_u}{\sum_k w_k} \right) . References ---------- .. [1] Fan Chung and L. Lu, Connected components in random graphs with given expected degree sequences, Ann. Combinatorics, 6, pp. 125-145, 2002. .. [2] Joel Miller and Aric Hagberg, Efficient generation of networks with given expected degrees, in Algorithms and Models for the Web-Graph (WAW 2011), Alan Frieze, Paul Horn, and PaweÅ‚ PraÅ‚at (Eds), LNCS 6732, pp. 115-126, 2011. iitkeytreversecss%|]\}}||dfVqdS(iN((t.0tctuv((sr/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/degree_seq.pys fsN(RR RRRRRtfloatR tsortedt enumerateRtTruetdictRtinttmathtfloortlogR(twRt selfloopsR#R!trhoRtmappingtutvtseqtlasttfactortptrtq((sr/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/degree_seq.pyRsDG  $      6    cCs˜tj|ƒs!tjdƒ‚n|dk rN|jƒrNtjdƒ‚qNnt|ƒ}tj||ƒ}g}x!t|ƒD]}|jgƒqWd\}}}xS|D]K} | dkr¬|| j|ƒt || ƒ|| |d}}}q¬q¬W|dkr |Sd g|d} xV|dkrtx$t||ƒdkrQ|d8}q.W||dkrttjdƒ‚n||j ƒ} |d8}d} |} x’t|ƒD]„}x$t|| ƒdkrÓ| d8} q°W|| j ƒ}|j | |ƒ|d8}| dkr§| d|f| | <| d7} q§q§Wx?t| ƒD]1}| |\}}||j|ƒ|d7}q<WqWd|j ƒ|j ƒf|_|S( sŒReturn a simple graph with given degree sequence constructed using the Havel-Hakimi algorithm. Parameters ---------- deg_sequence: list of integers Each integer corresponds to the degree of a node (need not be sorted). create_using : graph, optional (default Graph) Return graph of this type. The instance will be cleared. Directed graphs are not allowed. Raises ------ NetworkXException For a non-graphical degree sequence (i.e. one not realizable by some simple graph). Notes ----- The Havel-Hakimi algorithm constructs a simple graph by successively connecting the node of highest degree to other nodes of highest degree, resorting remaining nodes by degree, and repeating the process. The resulting graph has a high degree-associativity. Nodes are labeled 1,.., len(deg_sequence), corresponding to their position in deg_sequence. The basic algorithm is from Hakimi [1]_ and was generalized by Kleitman and Wang [2]_. References ---------- .. [1] Hakimi S., On Realizability of a Set of Integers as Degrees of the Vertices of a Linear Graph. I, Journal of SIAM, 10(3), pp. 496-506 (1962) .. [2] Kleitman D.J. and Wang D.L. Algorithms for Constructing Graphs and Digraphs with Given Valences and Factors Discrete Mathematics, 6(1), pp. 79-88 (1973) sInvalid degree sequences!Directed graphs are not supportediisNon-graphical integer sequences$havel_hakimi_graph %d nodes %d edgesN(iii(ii(R tis_valid_degree_sequenceR RRRRRRRRRRRR(RRRHR!tnum_degsR$tdmaxtdsumR#tdtmodstubsR/tmslentkR0tstubvalt stubtarget((sr/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/degree_seq.pyRsT'     ,    cCsêtjj|ƒst‚tjj|ƒs0t‚|d krKtjƒ}nddt|ƒt|ƒf\}}}}t||ƒ}tj||ƒ}|dkr¦|Sd} gg} } xôt |ƒD]æ} d \} }| |krñ|| }n| |kr || } n| dks"|dkr4tj dƒ‚n|| ||t| | ƒ}}} | dkr†| j d|d| | fƒqÆ|dkrÆ| j d|| fƒqÆqÆW||krÎtj dƒ‚nt j | ƒt j | ƒd g| d}xË| rÆt j| ƒ\}}}|d9}|t| ƒt| ƒkrRtj dƒ‚nd}xát |ƒD]Ó}| r²| s”| dd| ddkr²t j| ƒ\}}d}nt j| ƒ\}}}|dkrètj dƒ‚n|j||ƒ|ddks|dkre|d||f||<|d7}qeqeWx_t |ƒD]Q}||}|ddkr|t j| |ƒqIt j| |d|dfƒqIW|dkrüt j| ||fƒqüqüWd|jƒ|jƒf|_|S( sReturn a directed graph with the given degree sequences. Parameters ---------- in_deg_sequence : list of integers Each list entry corresponds to the in-degree of a node. out_deg_sequence : list of integers Each list entry corresponds to the out-degree of a node. create_using : graph, optional (default DiGraph) Return graph of this type. The instance will be cleared. Returns ------- G : DiGraph A graph with the specified degree sequences. Nodes are labeled starting at 0 with an index corresponding to the position in deg_sequence Raises ------ NetworkXError If the degree sequences are not digraphical. See Also -------- configuration_model Notes ----- Algorithm as described by Kleitman and Wang [1]_. References ---------- .. [1] D.J. Kleitman and D.L. Wang Algorithms for Constructing Graphs and Digraphs with Given Valences and Factors Discrete Mathematics, 6(1), pp. 79-88 (1973) is;Invalid degree sequences. Sequence values must be positive.iÿÿÿÿs9Invalid degree sequences. Sequences must have equal sums.is Non-digraphical integer sequenceis-directed_havel_hakimi_graph %d nodes %d edgesN(ii(iii(R tutilstis_list_of_intstAssertionErrorRtDiGraphRRRRR RtheapqtheapifytheappopRtheappushRRR(tin_deg_sequencetout_deg_sequenceRtsumintsumoutR+R,tmaxnR!tmaxintstubheaptzeroheapR#tin_degtout_degRPtfreeouttfreeinR0RQR$tstuboutt stubsourcetstubintstub((sr/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/degree_seq.pyRàsr( *        % !       )   " c Csyt|ƒt|ƒddks2tjdƒ‚n|d k r\|jƒr\tjdƒ‚nt|ƒdkr„tjd|ƒ}|Sg|D]}|dkr‹|^q‹}|jdtƒt|ƒd}tj ||ƒ}|}xct d|dƒD]N}|j ƒd}x+t |||ƒD]} |j || ƒqW||7}qõWt|j ƒƒt|ƒkru|jdƒn|S( s Make a tree for the given degree sequence. A tree has #nodes-#edges=1 so the degree sequence must have len(deg_sequence)-sum(deg_sequence)/2=1 g@gð?sDegree sequence invalidsDirected Graph not supportediiR2iN(RR R R RRRtsortR9t path_graphRRRtdegreet remove_node( RRR!tstdegR#RFR/tnedgesR0((sr/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/degree_seq.pyR Qs( %i cCset|d|ƒ}x9t|ƒD]+}y|jƒSWqtjk rIqXqWtjd|ƒ‚dS(s¤Return a simple random graph with the given degree sequence. If the maximum degree `d_m` in the sequence is `O(m^{1/4})` then the algorithm produces almost uniform random graphs in `O(m d_m)` time where `m` is the number of edges. Parameters ---------- sequence : list of integers Sequence of degrees seed : hashable object, optional Seed for random number generator tries : int, optional Maximum number of tries to create a graph Returns ------- G : Graph A graph with the specified degree sequence. Nodes are labeled starting at 0 with an index corresponding to the position in the sequence. Raises ------ NetworkXUnfeasible If the degree sequence is not graphical. NetworkXError If a graph is not produced in specified number of tries See Also -------- is_valid_degree_sequence, configuration_model Notes ----- The generator algorithm [1]_ is not guaranteed to produce a graph. References ---------- .. [1] Moshen Bayati, Jeong Han Kim, and Amin Saberi, A sequential algorithm for generating random graphs. Algorithmica, Volume 58, Number 4, 860-910, DOI: 10.1007/s00453-009-9340-1 Examples -------- >>> sequence = [1, 2, 2, 3] >>> G = nx.random_degree_sequence_graph(sequence) >>> sorted(G.degree().values()) [1, 2, 2, 3] Rs$failed to generate graph in %d triesN(tDegreeSequenceRandomGraphRtgenerateR tNetworkXUnfeasibleR (tsequenceRttriestDSRGttry_n((sr/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/degree_seq.pyR xs4RtcBs_eZd d„Zd„Zd d„Zd„Zd„Zd„Zd„Z d„Z d„Z RS( cCs™tj|ƒs!tjdƒ‚n|dk r=tj|ƒnt|ƒ|_t|jƒd|_ yt |jƒ|_ Wnt k r”d|_ nXdS(Ns degree sequence is not graphicalg@i( R RKRvRRRtlistRoR tmRRMt ValueError(tselfRoR((sr/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/degree_seq.pyt__init__·s  cCs¶tt|jƒƒ|_tjƒ|_|jj|jƒx<t|jj ƒƒD]%\}}|dkrP|j|=qPqPWt |jƒdkr¯|j ƒ|j ƒ|j ƒn|jS(Ni(R:R8Rotremaining_degreeR tGraphtgraphtadd_nodes_fromR{titemsRtphase1tphase2tphase3(R~R#RO((sr/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/generators/degree_seq.pyRuÄs"    cCsÁ|dk r|j||ƒn|j|dkr[|j|=|dk rn|j|ƒqnn|j|cd8<|j|dkrª|j|=|dk r½|j|ƒq½n|j|cd8s4       u~l a o '<