  The articulation points of an undirected connected graphs are those vertices
whose removal increases the number of connected components of the graph, i.e.
the vertices whose removal disconnects the graph. However, not all the
articulation points are equal: the removal of some of them might end in a
single vertex disconnected from the graph, whilst in other cases the graph can
be split in several small pieces. In order to measure the effect of the removal
of an articulation point, in \cite{AFL12} has been proposed the impact, defined
as the number of vertices that get disconnected from the main (largest)
surviving connected component (CC). In this paper we present the first linear
time algorithm ($\mathcal{O}(m+n)$ for a graph with $n$ vertices and $m$ edges)
to compute the impact of all the articulation points of the graph, thus
improving from the $\mathcal{O}(a(m+n))\approx\mathcal{O}(nm+n^2)$ of the
na\"ive algorithm, with $a$ being the number of articulation points of the
graph.
