The vulnerability measures on a connected graph which are mostly used and known are based on the Neighbourhood concept. Neighbour-integrity, edge-integrity and accessibility number are some of these measures. In this work we define and examine Common-neighbourhood of a connected graph as a new global connectivity measure. Our measure examines the neighbourhoods of all pairs of vertices of any connected graph. We show that, for connected graphs G(1) and G(2) of same order, if the dominating number of G(1) is bigger than the dominating number of G(2), then the common-neighbourhood of G(1) is less than the common-neighbourhood of G(2). We give some theorems and obtain some results on common-neighbourhood of a graph.