<p>Security is an important area of concern in the designing of a network and can be studied by the convexity structure of the corresponding graphs. The two widely studied notions of convexity in graphs are the geodesic convexity and the minimal path convexity. In this paper, we study some convexity parameters of Sierpiński graphs. It is also shown that Sierpiński graphs are interval monotone with respect to geodesic as well as minimal path convexity and are poly-convex with respect to geodesic convexity only.</p>