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In graph theory, connectivity refers to the minimum number of elements (nodes or edges) that need to be removed to disconnect the remaining nodes from each other.

An articulation point (or cut vertex) in a graph is a vertex whose removal increases the number of connected components in the graph.

Edge connectivity of a graph $G$ is the minimum number of edges that must be removed to make the graph disconnected.

Vertex connectivity of a graph $G$ is the minimum number of vertices whose removal results in a graph that is either disconnected or has only one vertex left.

A bridge is an edge in a connected graph, whose removal would cause the graph to become disconnected, separating it into two components.

A cut-set is a set of edges whose removal increases the number of connected components in the graph, effectively disconnecting the graph.

In directed graphs, connectivity is based on the direction of the edges, and separate measures exist such as 'strong connectivity' where every node can reach every other node following the direction of the edges, and 'weak connectivity' which ignores edge direction.