<p><b>Abstract</b>—A combined (2<it>log</it>N − 1)-stage interconnection network (denoted by <tmath>$\Delta \oplus \Delta '$</tmath>) is constructed by concatenating two Omega-equivalent networks (Δ and Δ′) with the rightmost stage of Δ and the leftmost stage of Δ′ overlapped. Benes network and the (2<it>log</it>N − 1)-stage shuffle-exchange network are two examples of such networks. Although these two networks have received intensive studies, the research on the topology of entire class of <tmath>$\Delta \oplus \Delta '$</tmath> networks is very limited so far. In this paper, we study the topological structure of <tmath>$\Delta \oplus \Delta '$</tmath> networks and propose an algorithm for determining topological equivalence between two given <tmath>$\Delta \oplus \Delta '$</tmath> networks. We also present a simplified Ω-equivalence checking algorithm as a supporting result.</p>