Components

Connectivity

is_connected(G)	Returns True if the graph is connected, False otherwise.
number_connected_components(G)	Returns the number of connected components.
connected_components(G)	Generate connected components.
node_connected_component(G, n)	Returns the set of nodes in the component of graph containing node n.

Strong connectivity

is_strongly_connected(G)	Test directed graph for strong connectivity.
number_strongly_connected_components(G)	Returns number of strongly connected components in graph.
strongly_connected_components(G)	Generate nodes in strongly connected components of graph.
strongly_connected_components_recursive(G)	Generate nodes in strongly connected components of graph.
kosaraju_strongly_connected_components(G[, …])	Generate nodes in strongly connected components of graph.
condensation(G[, scc])	Returns the condensation of G.

Weak connectivity

is_weakly_connected(G)	Test directed graph for weak connectivity.
number_weakly_connected_components(G)	Returns the number of weakly connected components in G.
weakly_connected_components(G)	Generate weakly connected components of G.

Attracting components

is_attracting_component(G)	Returns True if G consists of a single attracting component.
number_attracting_components(G)	Returns the number of attracting components in G.
attracting_components(G)	Generates the attracting components in G.

Biconnected components

is_biconnected(G)	Returns True if the graph is biconnected, False otherwise.
biconnected_components(G)	Returns a generator of sets of nodes, one set for each biconnected component of the graph
biconnected_component_edges(G)	Returns a generator of lists of edges, one list for each biconnected component of the input graph.
articulation_points(G)	Yield the articulation points, or cut vertices, of a graph.

Semiconnectedness

is_semiconnected(G[, topo_order])

Returns True if the graph is semiconnected, False otherwise.