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This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA )2 ADJ_DIRECTED ADJ_LOWERADJ_MAXADJ_MINADJ_PLUSADJ_UNDIRECTED ADJ_UPPERALL ARPACKOptionsBFSIterBLISS_FBLISS_FL BLISS_FLMBLISS_FMBLISS_FS BLISS_FSMDFSIterEdgeGET_ADJACENCY_BOTHGET_ADJACENCY_LOWERGET_ADJACENCY_UPPER GraphBaseIN InternalErrorOUTREWIRING_SIMPLEREWIRING_SIMPLE_LOOPSSTAR_IN STAR_MUTUALSTAR_OUTSTAR_UNDIRECTEDSTRONGTRANSITIVITY_NANTRANSITIVITY_ZEROTREE_INTREE_OUTTREE_UNDIRECTEDVertexWEAKarpack_optionscommunity_to_membership convex_hullis_degree_sequence is_graphicalis_graphical_degree_sequenceset_progress_handlerset_random_number_generatorset_status_handlerumap_compute_weights__igraph_version__)_get_adjacency_get_adjacency_sparse _get_adjlist_get_incidence _get_inclist)_count_automorphisms_vf2_get_automorphisms_vf2) _add_edge _add_edges _add_vertex _add_vertices 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_construct_graph_from_graph_tool_export_graph_to_graph_tool)!_construct_random_geometric_graph)_construct_bipartite_graph$_construct_incidence_bipartite_graph_construct_full_bipartite_graph!_construct_random_bipartite_graph)_write_graph_to_svg)Layout_layout _layout_auto_layout_sugiyama_layout_method_wrapper_3d_version_for_layout_mapping)Matching)disjoint_unionunion intersectionoperator_method_registry)EdgeSeq VertexSeq_add_proxy_methods)FittedPowerLaw Histogram RunningMeanmeanmedian percentilequantile power_law_fit) _indegree _outdegree_degree_distribution _pagerank_shortest_paths) GraphSummarysummary) deprecatednumpy_to_contiguous_memoryviewrescale) __version____version_info__Ncs(eZdZdZejZejZej Z ej Z ej ZejZejZejZejZejZeZeZejZfddZeeZe Z!ee"Z#e$Z%ee&Z'e(Z)ee*Z+e,Z-ee.Z/e0Z1ee2Z3e4Z5ee6Z7e8Z9e:Z;ee<Z=e=Z>e?Z@e@ZAeeBZCeDZEeeFZGeHZIeeJZKeLZMeeNZOePZQeeRZSeeTZUeeVZWeXZYeZZ[ee\Z]ee^Z_ee`ZaeebZceedZeeefZgddZhd8dd Zid d Zjd d ZkelddZmelddZneoZpeqZresZteuZvewZxeyZze{Z|e}Z~edZedZedZedZedZedZedZedZedZedZeZeZeZeZeZeZeZeZeZeZeZeZeZeZeZeZ eZeZeZeZeZeZeZeZeZeZeZeZeZeZeZeZeZeZeZeZeZeZeZeZeZeZeZd9ddZd:d!d"Zefd#d$Zd;d%d&Zd'd(Zd)d*Zd>> g = Graph.Full(3) >>> g["name"] = "Triangle graph" >>> g["name"] 'Triangle graph' >>> del g["name"] When a graph is indexed by a pair of vertex indices or names, the graph itself is treated as an adjacency matrix and the corresponding cell of the matrix is returned: >>> g = Graph.Full(3) >>> g.vs["name"] = ["A", "B", "C"] >>> g[1, 2] 1 >>> g["A", "B"] 1 >>> g["A", "B"] = 0 >>> g.ecount() 2 Assigning values different from zero or one to the adjacency matrix will be translated to one, unless the graph is weighted, in which case the numbers will be treated as weights: >>> g.is_weighted() False >>> g["A", "B"] = 2 >>> g["A", "B"] 1 >>> g.es["weight"] = 1.0 >>> g.is_weighted() True >>> g["A", "B"] = 2 >>> g["A", "B"] 2 >>> g.es["weight"] [1.0, 1.0, 2] cs|dd}d}dgdiiig}t|}|||rRtd|jj|t|}t |dkrt |ddr| d|d||dt |<t |D]\}}||kr||||<q|\} } } } } }| dkrd} | dkrg} z,ddl m}m}t| ||fr t| } Wntk r$YnX|rszGraph.dfs..)rrT)vcountranger neighborsr) rZvidrnvaddedstackZvidsparentsr(Zneighborrrrdfss(        z Graph.dfscCs"t||}|r|j|ddS|S)aCalculates a minimum spanning tree for a graph. @param weights: a vector containing weights for every edge in the graph. C{None} means that the graph is unweighted. @param return_tree: whether to return the minimum spanning tree (when C{return_tree} is C{True}) or to return the IDs of the edges in the minimum spanning tree instead (when C{return_tree} is C{False}). The default is C{True} for historical reasons as this argument was introduced in igraph 0.6. @return: the spanning tree as a L{Graph} object if C{return_tree} is C{True} or the IDs of the edges that constitute the spanning tree if C{return_tree} is C{False}. @newfield ref: Reference @ref: Prim, R.C.: I{Shortest connection networks and some generalizations}. Bell System Technical Journal 36:1389-1401, 1957. F)Zdelete_vertices)rZ_spanning_treeZsubgraph_edges)rweightsZ return_treerrrr spanning_trees zGraph.spanning_treecOsttj|f||S)aCalculates the dyad census of the graph. Dyad census means classifying each pair of vertices of a directed graph into three categories: mutual (there is an edge from I{a} to I{b} and also from I{b} to I{a}), asymmetric (there is an edge from I{a} to I{b} or from I{b} to I{a} but not the other way round) and null (there is no connection between I{a} and I{b}). @return: a L{DyadCensus} object. @newfield ref: Reference @ref: Holland, P.W. and Leinhardt, S. (1970). A Method for Detecting Structure in Sociometric Data. American Journal of Sociology, 70, 492-513. )rr dyad_censusrrrrrrr0+szGraph.dyad_censuscOsttj|f||S)a{Calculates the triad census of the graph. @return: a L{TriadCensus} object. @newfield ref: Reference @ref: Davis, J.A. and Leinhardt, S. (1972). The Structure of Positive Interpersonal Relations in Small Groups. In: J. Berger (Ed.), Sociological Theories in Progress, Volume 2, 218-251. Boston: Houghton Mifflin. )rr triad_censusr1rrrr2<s zGraph.triad_censusnancCs6|dkrt||S|j||d}t|tt|S)aCalculates the average of the vertex transitivities of the graph. In the unweighted case, the transitivity measures the probability that two neighbors of a vertex are connected. In case of the average local transitivity, this probability is calculated for each vertex and then the average is taken. Vertices with less than two neighbors require special treatment, they will either be left out from the calculation or they will be considered as having zero transitivity, depending on the I{mode} parameter. The calculation is slightly more involved for weighted graphs; in this case, weights are taken into account according to the formula of Barrat et al (see the references). Note that this measure is different from the global transitivity measure (see L{transitivity_undirected()}) as it simply takes the average local transitivity across the whole network. @param mode: defines how to treat vertices with degree less than two. If C{TRANSITIVITY_ZERO} or C{"zero"}, these vertices will have zero transitivity. If C{TRANSITIVITY_NAN} or C{"nan"}, these vertices will be excluded from the average. @param weights: edge weights to be used. Can be a sequence or iterable or even an edge attribute name. @see: L{transitivity_undirected()}, L{transitivity_local_undirected()} @newfield ref: Reference @ref: Watts DJ and Strogatz S: I{Collective dynamics of small-world networks}. Nature 393(6884):440-442, 1998. @ref: Barrat A, Barthelemy M, Pastor-Satorras R and Vespignani A: I{The architecture of complex weighted networks}. PNAS 101, 3747 (2004). U{http://arxiv.org/abs/cond-mat/0311416}. 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