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Cut-vertices (articulation points) in Graph Theory → Read more...
A vertex $v$ in a connected graph $G$ is called a cut-vertex if $G - v$ results in a disconnected graph, note that $G - v$ is an induced subgraph of $G$ (meaning that $G - v$ contains all the vertices of $G$ but $v$ and a set of edges $G - V$ where $V$ consists of all the edges incident to $v$).
In this article I implement an algorthm to find the articulation points in an undirected graph, also I explain biconnected components in an undirected graph and explain concepts such as edge connectivity and vertex connectivity.