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 igraph: Network Analysis and Visualization
 articulation_points: Articulation points of a graph
Articulation points of a graph
Description
Articuation points or cut vertices are vertices whose removal increases the number of connected components in a graph.
Usage
1 
Arguments
graph 
The input graph. It is treated as an undirected graph, even if it is directed. 
Details
Articuation points or cut vertices are vertices whose removal increases the number of connected components in a graph. If the original graph was connected, then the removal of a single articulation point makes it undirected. If a graph contains no articulation points, then its vertex connectivity is at least two.
Value
A numeric vector giving the vertex ids of the articulation points of the input graph.
Author(s)
Gabor Csardi csardi.gabor@gmail.com
See Also
biconnected_components
, components
,
is_connected
, vertex_connectivity
Examples
1 2 3 4  g < disjoint_union( make_full_graph(5), make_full_graph(5) )
clu < components(g)$membership
g < add_edges(g, c(match(1, clu), match(2, clu)) )
articulation_points(g)

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 aaaigraphpackage: The igraph package
 add_edges: Add edges to a graph
 add_layout_: Add layout to graph
 add_vertices: Add vertices to a graph
 adjacent_vertices: Adjacent vertices of multiple vertices in a graph
 all_simple_paths: List all simple paths from one source
 alpha_centrality: Find Bonacich alpha centrality scores of network positions
 are_adjacent: Are two vertices adjacent?
 arpack: ARPACK eigenvector calculation
 articulation_points: Articulation points of a graph
 as_adjacency_matrix: Convert a graph to an adjacency matrix
 as_adj_list: Adjacency lists
 as.directed: Convert between directed and undirected graphs
 as_edgelist: Convert a graph to an edge list
 as_graphnel: Convert igraph graphs to graphNEL objects from the graph...
 as_ids: Convert a vertex or edge sequence to an ordinary vector
 as.igraph: Conversion to igraph
 as_incidence_matrix: Incidence matrix of a bipartite graph
 as_long_data_frame: Convert a graph to a long data frame
 as_membership: Declare a numeric vector as a membership vector
 assortativity: Assortativity coefficient
 authority_score: Kleinberg's authority centrality scores.
 automorphisms: Number of automorphisms
 betweenness: Vertex and edge betweenness centrality
 bfs: Breadthfirst search
 biconnected_components: Biconnected components
 bipartite_mapping: Decide whether a graph is bipartite
 bipartite_projection: Project a bipartite graph
 canonical_permutation: Canonical permutation of a graph
 categorical_pal: Palette for categories
 centralize: Centralization of a graph
 centr_betw: Centralize a graph according to the betweenness of vertices
 centr_betw_tmax: Theoretical maximum for betweenness centralization
 centr_clo: Centralize a graph according to the closeness of vertices
 centr_clo_tmax: Theoretical maximum for closeness centralization
 centr_degree: Centralize a graph according to the degrees of vertices
 centr_degree_tmax: Theoretical maximum for degree centralization
 centr_eigen: Centralize a graph according to the eigenvector centrality of...
 centr_eigen_tmax: Theoretical maximum for betweenness centralization
 c.igraph.es: Concatenate edge sequences
 c.igraph.vs: Concatenate vertex sequences
 cliques: The functions find cliques, ie. complete subgraphs in a graph
 closeness: Closeness centrality of vertices
 cluster_edge_betweenness: Community structure detection based on edge betweenness
 cluster_fast_greedy: Community structure via greedy optimization of modularity
 cluster_infomap: Infomap community finding
 cluster_label_prop: Finding communities based on propagating labels
 cluster_leading_eigen: Community structure detecting based on the leading...
 cluster_louvain: Finding community structure by multilevel optimization of...
 cluster_optimal: Optimal community structure
 cluster_spinglass: Finding communities in graphs based on statistical meachanics
 cluster_walktrap: Community strucure via short random walks
 cocitation: Cocitation coupling
 cohesive_blocks: Calculate Cohesive Blocks
 communities: Functions to deal with the result of network community...
 compare: Compares community structures using various metrics
 complementer: Complementer of a graph
 components: Connected components of a graph
 component_wise: Componentwise layout
 compose: Compose two graphs as binary relations
 consensus_tree: Create a consensus tree from several hierarchical random...
 console: The igraph console
 constraint: Burt's constraint
 contract: Contract several vertices into a single one
 convex_hull: Convex hull of a set of vertices
 coreness: Kcore decomposition of graphs
 count_isomorphisms: Count the number of isomorphic mappings between two graphs
 count_motifs: Graph motifs
 count_subgraph_isomorphisms: Count the isomorphic mappings between a graph and the...
 count_triangles: Find triangles in graphs
 curve_multiple: Optimal edge curvature when plotting graphs
 decompose: Decompose a graph into components
 degree: Degree and degree distribution of the vertices
 delete_edge_attr: Delete an edge attribute
 delete_edges: Delete edges from a graph
 delete_graph_attr: Delete a graph attribute
 delete_vertex_attr: Delete a vertex attribute
 delete_vertices: Delete vertices from a graph
 dfs: Depthfirst search
 diameter: Diameter of a graph
 difference: Difference of two sets
 difference.igraph: Difference of graphs
 difference.igraph.es: Difference of edge sequences
 difference.igraph.vs: Difference of vertex sequences
 dim_select: Dimensionality selection for singular values using profile...
 disjoint_union: Disjoint union of graphs
 distances: Shortest (directed or undirected) paths between vertices
 diverging_pal: Diverging palette
 diversity: Graph diversity
 dominator_tree: Dominator tree
 dyad_census: Dyad census of a graph
 E: Edges of a graph
 each_edge: Rewires the endpoints of the edges of a graph to a random...
 eccentricity: Eccentricity of the vertices in a graph
 edge: Helper function for adding and deleting edges
 edge_attr: Query edge attributes of a graph
 edge_attr_names: List names of edge attributes
 edge_attrset: Set one or more edge attributes
 edge_connectivity: Edge connectivity.
 edge_density: Graph density
 ego: Neighborhood of graph vertices
 eigen_centrality: Find Eigenvector Centrality Scores of Network Positions
 embed_adjacency_matrix: Spectral Embedding of Adjacency Matrices
 embed_laplacian_matrix: Spectral Embedding of the Laplacian of a Graph
 ends: Incident vertices of some graph edges
 erdos.renyi.game: Generate random graphs according to the ErdosRenyi model
 fit_hrg: Fit a hierarchical random graph model
 fit_power_law: Fitting a powerlaw distribution function to discrete data
 gclust.app: Graph Clustering Using NMF (and no SVT)  Apparent Clusters
 gclust.rsvt: Graph Clustering Using SVT and NMF  Clusters Implied by...
 getAICc: Compute AIC based on a Poisson Approximation using the output...
 get.edge.ids: Find the edge ids based on the incident vertices of the edges
 girth: Girth of a graph
 gorder: Order (number of vertices) of a graph
 graph_: Convert object to a graph
 graph_attr: Graph attributes of a graph
 graph_attr_names: List names of graph attributes
 graph_attrset: Set all or some graph attributes
 graph_from_adjacency_matrix: Create graphs from adjacency matrices
 graph_from_adj_list: Create graphs from adjacency lists
 graph_from_atlas: Create a graph from the Graph Atlas
 graph_from_data_frame: Creating igraph graphs from data frames or viceversa
 graph_from_edgelist: Create a graph from an edge list matrix
 graph_from_graphdb: Load a graph from the graph database for testing graph...
 graph_from_graphnel: Convert graphNEL objects from the graph package to igraph
 graph_from_incidence_matrix: Create graphs from an incidence matrix
 graph_from_isomorphism_class: Create a graph from an isomorphism class
 graph_from_lcf: Creating a graph from LCF notation
 graph_from_literal: Creating (small) graphs via a simple interface
 graphlet_basis: Graphlet decomposition of a graph
 graph_version: Igraph data structure versions
 groups: Groups of a vertex partitioning
 gsize: The size of the graph (number of edges)
 head_of: Head of the edge(s) in a graph
 hrg: Create a hierarchical random graph from an igraph graph
 hrgmethods: Hierarchical random graphs
 hrg_tree: Create an igraph graph from a hierarchical random graph model
 hub_score: Kleinberg's hub centrality scores.
 identical_graphs: Decide if two graphs are identical
 igraphattributecombination: How igraph functions handle attributes when the graph changes
 igraph_demo: Run igraph demos, step by step
 igraphdollar: Getting and setting graph attributes, shortcut
 igraphesattributes: Query or set attributes of the edges in an edge sequence
 igraphesindexing: Indexing edge sequences
 igraphesindexing2: Select edges and show their metadata
 igraphminus: Delete vertices or edges from a graph
 igraph_options: Parameters for the igraph package
 igraph_test: Run package tests
 igraph_version: Query igraph's version string
 igraphvsattributes: Query or set attributes of the vertices in a vertex sequence
 igraphvsindexing: Indexing vertex sequences
 igraphvsindexing2: Select vertices and show their metadata
 incident: Incident edges of a vertex in a graph
 incident_edges: Incident edges of multiple vertices in a graph
 intersection: Intersection of two or more sets
 intersection.igraph: Intersection of graphs
 intersection.igraph.es: Intersection of edge sequences
 intersection.igraph.vs: Intersection of vertex sequences
 is_chordal: Chordality of a graph
 is_dag: Directed acyclic graphs
 is_degseq: Check if a degree sequence is valid for a multigraph
 is_directed: Check whether a graph is directed
 is_graphical: Is a degree sequence graphical?
 is_igraph: Is this object an igraph graph?
 is_min_separator: Minumal vertex separators
 is_named: Named graphs
 isomorphic: Decide if two graphs are isomorphic
 isomorphism_class: Isomorphism class of a graph
 isomorphisms: Calculate all isomorphic mappings between the vertices of two...
 is_separator: Vertex separators
 is_weighted: Weighted graphs
 ivs: Independent vertex sets
 keeping_degseq: Graph rewiring while preserving the degree distribution
 knn: Average nearest neighbor degree
 laplacian_matrix: Graph Laplacian
 layout_: Graph layouts
 layout_as_bipartite: Simple tworow layout for bipartite graphs
 layout_as_star: Generate coordinates to place the vertices of a graph in a...
 layout_as_tree: The ReingoldTilford graph layout algorithm
 layout.deprecated: Deprecated layout functions
 layout.fruchterman.reingold.grid: Grid FruchtermanReingold layout, this was removed from...
 layout_in_circle: Graph layout with vertices on a circle.
 layout_nicely: Choose an appropriate graph layout algorithm automatically
 layout_on_grid: Simple grid layout
 layout_on_sphere: Graph layout with vertices on the surface of a sphere
 layout_randomly: Randomly place vertices on a plane or in 3d space
 layout.spring: Spring layout, this was removed from igraph
 layout.svd: SVD layout, this was removed from igraph
 layout_with_dh: The DavidsonHarel layout algorithm
 layout_with_drl: The DrL graph layout generator
 layout_with_fr: The FruchtermanReingold layout algorithm
 layout_with_gem: The GEM layout algorithm
 layout_with_graphopt: The graphopt layout algorithm
 layout_with_kk: The KamadaKawai layout algorithm
 layout_with_lgl: Large Graph Layout
 layout_with_mds: Graph layout by multidimensional scaling
 layout_with_sugiyama: The Sugiyama graph layout generator
 local_scan: Compute local scan statistics on graphs
 make_: Make a new graph
 make_bipartite_graph: Create a bipartite graph
 make_chordal_ring: Create an extended chordal ring graph
 make_clusters: Creates a communities object.
 make_de_bruijn_graph: De Bruijn graphs
 make_empty_graph: A graph with no edges
 make_full_bipartite_graph: Create a full bipartite graph
 make_full_citation_graph: Create a complete (full) citation graph
 make_full_graph: Create a full graph
 make_graph: Create an igraph graph from a list of edges, or a notable...
 make_kautz_graph: Kautz graphs
 make_lattice: Create a lattice graph
 make_line_graph: Line graph of a graph
 make_ring: Create a ring graph
 make_star: Create a star graph, a tree with n vertices and n  1 leaves
 make_tree: Create tree graphs
 matching: Graph matching
 match_vertices: Match Graphs given a seeding of vertex correspondences
 max_cardinality: Maximum cardinality search
 max_flow: Maximum flow in a graph
 merge_coords: Merging graph layouts
 min_cut: Minimum cut in a graph
 min_separators: Minimum size vertex separators
 min_st_separators: Minimum size vertex separators
 modularity.igraph: Modularity of a community structure of a graph
 motifs: Graph motifs
 mst: Minimum spanning tree
 neighbors: Neighboring (adjacent) vertices in a graph
 nexus: Query and download from the Nexus network repository
 normalize: Normalize layout
 norm_coords: Normalize coordinates for plotting graphs
 page_rank: The Page Rank algorithm
 path: Helper function to add or delete edges along a path
 permute: Permute the vertices of a graph
 pipe: Magrittr's pipes
 plot.common: Drawing graphs
 plot_dendrogram.communities: Community structure dendrogram plots
 plot_dendrogram.igraphHRG: HRG dendrogram plot
 plot.igraph: Plotting of graphs
 plot.sir: Plotting the results on multiple SIR model runs
 plus.igraph: Add vertices, edges or another graph to a graph
 power_centrality: Find Bonacich Power Centrality Scores of Network Positions
 predict_edges: Predict edges based on a hierarchical random graph model
 print.igraph: Print graphs to the terminal
 print.igraph.es: Print an edge sequence to the screen
 print.igraphHRG: Print a hierarchical random graph model to the screen
 print.igraphHRGConsensus: Print a hierarchical random graph consensus tree to the...
 print.igraph.vs: Show a vertex sequence on the screen
 radius: Radius of a graph
 random_walk: Random walk on a graph
 read_graph: Reading foreign file formats
 reciprocity: Reciprocity of graphs
 rep.igraph: Replicate a graph multiple times
 rev.igraph.es: Reverse the order in an edge sequence
 rev.igraph.vs: Reverse the order in a vertex sequence
 rewire: Rewiring edges of a graph
 rglplot: 3D plotting of graphs with OpenGL
 r_pal: The default R palette
 running_mean: Running mean of a time series
 sample_: Sample from a random graph model
 sample_bipartite: Bipartite random graphs
 sample_correlated_gnp: Generate a new random graph from a given graph by randomly...
 sample_correlated_gnp_pair: Sample a pair of correlated G(n,p) random graphs
 sample_degseq: Generate random graphs with a given degree sequence
 sample_dirichlet: Sample from a Dirichlet distribution
 sample_dot_product: Generate random graphs according to the random dot product...
 sample_fitness: Random graphs from vertex fitness scores
 sample_fitness_pl: Scalefree random graphs, from vertex fitness scores
 sample_forestfire: Forest Fire Network Model
 sample_gnm: Generate random graphs according to the G(n,m) ErdosRenyi...
 sample_gnp: Generate random graphs according to the G(n,p) ErdosRenyi...
 sample_grg: Geometric random graphs
 sample_growing: Growing random graph generation
 sample_hierarchical_sbm: Sample the hierarchical stochastic block model
 sample_hrg: Sample from a hierarchical random graph model
 sample_islands: A graph with subgraphs that are each a random graph.
 sample_k_regular: Create a random regular graph
 sample_last_cit: Random citation graphs
 sample_motifs: Graph motifs
 sample_pa: Generate scalefree graphs according to the BarabasiAlbert...
 sample_pa_age: Generate an evolving random graph with preferential...
 sample_pref: Traitbased random generation
 sample_sbm: Sample stochastic block model
 sample_seq: Sampling a random integer sequence
 sample_smallworld: The WattsStrogatz smallworld model
 sample_sphere_surface: Sample vectors uniformly from the surface of a sphere
 sample_sphere_volume: Sample vectors uniformly from the volume of a sphere
 sample_traits_callaway: Graph generation based on different vertex types
 scan_stat: Scan statistics on a time series of graphs
 scg: Allinone Function for the SCG of Matrices and Graphs
 scg_eps: Error of the spectral coarse graining (SCG) approximation
 scg_group: SCG Problem Solver
 scgmethod: Spectral Coarse Graining
 scg_semi_proj: SemiProjectors
 sequential_pal: Sequential palette
 set_edge_attr: Set edge attributes
 set_graph_attr: Set a graph attribute
 set_vertex_attr: Set vertex attributes
 shapes: Various vertex shapes when plotting igraph graphs
 similarity: Similarity measures of two vertices
 simplified: Constructor modifier to drop multiple and loop edges
 simplify: Simple graphs
 sir: SIR model on graphs
 spectrum: Eigenvalues and eigenvectors of the adjacency matrix of a...
 split_join_distance: Splitjoin distance of two community structures
 srand: Deprecated function, used to set random seed of the C...
 st_cuts: List all (s,t)cuts of a graph
 st_min_cuts: List all minimum (s,t)cuts of a graph
 stochastic_matrix: Stochastic matrix of a graph
 strength: Strength or weighted vertex degree
 subcomponent: In or out component of a vertex
 subgraph: Subgraph of a graph
 subgraph_centrality: Find subgraph centrality scores of network positions
 subgraph_isomorphic: Decide if a graph is subgraph isomorphic to another one
 subgraph_isomorphisms: All isomorphic mappings between a graph and subgraphs of...
 sub.igraph: Query and manipulate a graph as it were an adjacency matrix
 subsub.igraph: Query and manipulate a graph as it were an adjacency list
 tail_of: Tails of the edge(s) in a graph
 tkigraph: Experimental basic igraph GUI
 tkplot: Interactive plotting of graphs
 topo_sort: Topological sorting of vertices in a graph
 transitivity: Transitivity of a graph
 triad_census: Triad census, subgraphs with three vertices
 unfold_tree: Convert a general graph into a forest
 union: Union of two or more sets
 union.igraph: Union of graphs
 union.igraph.es: Union of edge sequences
 union.igraph.vs: Union of vertex sequences
 unique.igraph.es: Remove duplicate edges from an edge sequence
 unique.igraph.vs: Remove duplicate vertices from a vertex sequence
 upgrade_graph: Igraph data structure versions
 V: Vertices of a graph
 vertex: Helper function for adding and deleting vertices
 vertex_attr: Query vertex attributes of a graph
 vertex_attr_names: List names of vertex attributes
 vertex_attrset: Set one or more vertex attributes
 vertex_connectivity: Vertex connectivity.
 vertex.shape.pie: Using pie charts as vertices in graph plots
 which_multiple: Find the multiple or loop edges in a graph
 which_mutual: Find mutual edges in a directed graph
 with_edge_: Constructor modifier to add edge attributes
 with_graph_: Constructor modifier to add graph attributes
 without_attr: Construtor modifier to remove all attributes from a graph
 without_loops: Constructor modifier to drop loop edges
 without_multiples: Constructor modifier to drop multiple edges
 with_vertex_: Constructor modifier to add vertex attributes
 write_graph: Writing the graph to a file in some format