This paper introduces the notion of the (r, s) incidence graph of an n-polytope P as the bipartite graph whose nodes correspond to the r-faces and the s-faces of P with an edge joining two nodes iff one of the corresponding faces contains the other. Various types of connectivity are defined for incidence graphs and bounds for these connectivities are established as functions of r, s, and n. It is shown that these bounds are also valid for a large class of cell-complexes.