Enumeration of 2-regular circulant graphs and directed double networks

We present a formula to enumerate non-isomorphic circulant digraphs of order nn with connection sets of cardinality 2. This formula simplifies to C(n,2)=3×2a−1−4C(n,2)=3×2a−1−4 in the case when n=2a(a≥3)n=2a(a≥3), and C(n,2)=(pa−1)(p+1)2(p−1)−a when n=pan=pa(where pp is an odd prime and a≥1a≥1). The number of non-isomorphic directed double networks are also enumerated.