is_connected#

is_connected(G)[source]#

Returns True if the graph is connected, False otherwise.

A graph is connected if, for every pair of distinct nodes, there is a path between them. If there is a pair of nodes for which such path does not exist, the graph is not connected (also referred to as “disconnected”).

A graph consisting of a single node and no edges is connected. Connectivity is undefined for the null graph (graph with no nodes).

Parameters:

GNetworkX Graph: An undirected graph.

Returns:

connectedbool: True if the graph is connected, False otherwise.

Raises:

NetworkXNotImplemented: If G is directed.

See also

is_strongly_connected
is_weakly_connected
is_semiconnected
is_biconnected
connected_components

Notes

This function is for undirected graphs only. For directed graphs, use is_strongly_connected() or is_weakly_connected().

The algorithm is based on a Breadth-First Search (BFS) traversal and its time complexity is \(O(n + m)\), where \(n\) is the number of nodes and \(m\) the number of edges in the graph.

Examples

>>> G = nx.path_graph(4)
>>> print(nx.is_connected(G))
True
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Additional backends implement this function

cugraph : GPU-accelerated backend.

graphblas : OpenMP-enabled sparse linear algebra backend.