Abstract. If G is a graph, then its P₂-path graph, P₂(G), has vertex set identical with the set of paths of length 2 in G, with two vertices adjacent in P₂(G) if and only if the union of corresponding paths forms either a path of length 3 or a triangle in G.

Let d be the minimum degree of G, d>2. We prove that if G is a connected graph, then P₂(G) is at least (d-1)-connected. However, if G is 2-connected, then P₂(G) is at least (2d-2)-connected.

We remark that if G is d-regular graph then P₂(G) is (2d-2)-regular, and hence if G is 2-connected then the connectivity of P₂(G) equals the degree. I.e., the connectivity is maximum possible.