Reliability and efficiency are important criteria in the design of interconnection networks. Recently, the w-wide diameter dw(G), the (w − 1)-fault diameter Dw(G), and the w-Rabin number rw(G) have been used to measure network reliability and efficiency. In this paper, we study dw(G), Dw(G) and rw(G) using the strong w-Rabin number r∗ w(G) for 1 ≤ w ≤ k(G) and G is a circulant network G(dn; {1,...