Growing Small-World Networks Generated by Attaching to Edges

We introduce a minimal model of small-world growing network generated by attaching to edges. The produced network is a plane graph which exists in real-life world. We obtain the analytic results of degree distribution decaying exponentially with degree and average clustering coefficient $C={3/2}ln3-1\approx 0.6479$, which are in good agreement with the numerical simulations. We also prove that the increasing tendency of average path length of the considered network is a little slower than the logarithm of the network order $N$.