ó |£*^c@sŽdZdjdddgƒZddddd d gZd d lZd „ZeZd d d„Z d d d„Z d d d„Z d d„Z d S(s Find the k-cores of a graph. The k-core is found by recursively pruning nodes with degrees less than k. See the following reference for details: An O(m) Algorithm for Cores Decomposition of Networks Vladimir Batagelj and Matjaz Zaversnik, 2003. http://arxiv.org/abs/cs.DS/0310049 s s Dan Schult (dschult@colgate.edu)s)Jason Grout (jason-sage@creativetrax.com)sAric Hagberg (hagberg@lanl.gov)t core_numbertk_coretk_shelltk_crusttk_coronat find_coresiÿÿÿÿNc sˆjƒrtjdƒ‚nˆjƒdkrEtjddƒ‚nˆjƒrrddl‰‡‡fd†‰n ˆj‰ˆjƒ}t|d|j ƒ}dg}d}xSt |ƒD]E\}}|||kr¸|j |g|||ƒ||}q¸q¸Wt d „t |ƒDƒƒ}|}t ‡fd †ˆDƒƒ} x¼|D]´}x«| |D]Ÿ} || ||krW| | j |ƒ|| } ||| } | || <| ||| <|| || || <|| <||| cd 7<|| cd 8Xsc3s'|]}|tˆ|ƒƒfVqdS(N(tset(RR (R (sl/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/core.pys [si(t is_multigraphtnxt NetworkXErrortnumber_of_selfloopst is_directedR tneighbors_itertdegreetsortedtgett enumeratetextendtdicttremove( R tdegreestnodestbin_boundariest curr_degreetiR tnode_postcoretnbrstuRt bin_start((R R R sl/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/core.pyRsD$           cskˆdkrtj|ƒ‰nˆdkr?tˆjƒƒ‰n‡‡fd†ˆDƒ}|j|ƒjƒS(sHReturn the k-core of G. A k-core is a maximal subgraph that contains nodes of degree k or more. Parameters ---------- G : NetworkX graph A graph or directed graph k : int, optional The order of the core. If not specified return the main core. core_number : dictionary, optional Precomputed core numbers for the graph G. Returns ------- G : NetworkX graph The k-core subgraph Raises ------ NetworkXError The k-core is not defined for graphs with self loops or parallel edges. Notes ----- The main core is the core with the largest degree. Not implemented for graphs with parallel edges or self loops. For directed graphs the node degree is defined to be the in-degree + out-degree. Graph, node, and edge attributes are copied to the subgraph. See Also -------- core_number References ---------- .. [1] An O(m) Algorithm for Cores Decomposition of Networks Vladimir Batagelj and Matjaz Zaversnik, 2003. http://arxiv.org/abs/cs.DS/0310049 c3s%|]}ˆ|ˆkr|VqdS(N((Rtn(Rtk(sl/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/core.pys œsN(tNoneRRtmaxtvaluestsubgraphtcopy(R R*RR ((RR*sl/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/core.pyRks -  cskˆdkrtj|ƒ‰nˆdkr?tˆjƒƒ‰n‡‡fd†ˆDƒ}|j|ƒjƒS(söReturn the k-shell of G. The k-shell is the subgraph of nodes in the k-core but not in the (k+1)-core. Parameters ---------- G : NetworkX graph A graph or directed graph. k : int, optional The order of the shell. If not specified return the main shell. core_number : dictionary, optional Precomputed core numbers for the graph G. Returns ------- G : NetworkX graph The k-shell subgraph Raises ------ NetworkXError The k-shell is not defined for graphs with self loops or parallel edges. Notes ----- This is similar to k_corona but in that case only neighbors in the k-core are considered. Not implemented for graphs with parallel edges or self loops. For directed graphs the node degree is defined to be the in-degree + out-degree. Graph, node, and edge attributes are copied to the subgraph. See Also -------- core_number k_corona References ---------- .. [1] A model of Internet topology using k-shell decomposition Shai Carmi, Shlomo Havlin, Scott Kirkpatrick, Yuval Shavitt, and Eran Shir, PNAS July 3, 2007 vol. 104 no. 27 11150-11154 http://www.pnas.org/content/104/27/11150.full c3s%|]}ˆ|ˆkr|VqdS(N((RR)(RR*(sl/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/core.pys ÕsN(R+RRR,R-R.R/(R R*RR ((RR*sl/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/core.pyRŸs 2  csoˆdkrtj|ƒ‰nˆdkrCtˆjƒƒd‰n‡‡fd†ˆDƒ}|j|ƒjƒS(sÿReturn the k-crust of G. The k-crust is the graph G with the k-core removed. Parameters ---------- G : NetworkX graph A graph or directed graph. k : int, optional The order of the shell. If not specified return the main crust. core_number : dictionary, optional Precomputed core numbers for the graph G. Returns ------- G : NetworkX graph The k-crust subgraph Raises ------ NetworkXError The k-crust is not defined for graphs with self loops or parallel edges. Notes ----- This definition of k-crust is different than the definition in [1]_. The k-crust in [1]_ is equivalent to the k+1 crust of this algorithm. Not implemented for graphs with parallel edges or self loops. For directed graphs the node degree is defined to be the in-degree + out-degree. Graph, node, and edge attributes are copied to the subgraph. See Also -------- core_number References ---------- .. [1] A model of Internet topology using k-shell decomposition Shai Carmi, Shlomo Havlin, Scott Kirkpatrick, Yuval Shavitt, and Eran Shir, PNAS July 3, 2007 vol. 104 no. 27 11150-11154 http://www.pnas.org/content/104/27/11150.full ic3s%|]}ˆ|ˆkr|VqdS(N((RR)(RR*(sl/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/core.pys sN(R+RRR,R-R.R/(R R*RR ((RR*sl/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/core.pyRØs /  csMˆdkrtjˆƒ‰n‡‡‡fd†ˆDƒ}ˆj|ƒjƒS(sReturn the k-corona of G. The k-corona is the subgraph of nodes in the k-core which have exactly k neighbours in the k-core. Parameters ---------- G : NetworkX graph A graph or directed graph k : int The order of the corona. core_number : dictionary, optional Precomputed core numbers for the graph G. Returns ------- G : NetworkX graph The k-corona subgraph Raises ------ NetworkXError The k-cornoa is not defined for graphs with self loops or parallel edges. Notes ----- Not implemented for graphs with parallel edges or self loops. For directed graphs the node degree is defined to be the in-degree + out-degree. Graph, node, and edge attributes are copied to the subgraph. See Also -------- core_number References ---------- .. [1] k -core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects, A. V. Goltsev, S. N. Dorogovtsev, and J. F. F. Mendes, Phys. Rev. E 73, 056101 (2006) http://link.aps.org/doi/10.1103/PhysRevE.73.056101 c3s^|]T}ˆ|ˆkrtgˆ|D]}ˆ|ˆkr'|^q'ƒˆkr|VqdS(N(tlen(RR)R (R RR*(sl/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/core.pys AsN(R+RRR.R/(R R*RR ((R RR*sl/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/core.pyRs0 ( t__doc__tjoint __author__t__all__tnetworkxRRRR+RRRR(((sl/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/core.pyt s    N497