  Hierarchical networks actually have many applications in the real world.
Firstly, we propose a new class of hierarchical networks with scale-free and
fractal structure, which are the networks with triangles compared to
traditional hierarchical networks. Secondly, we study the precise results of
some structural properties to derive small-world effect and scale-free feature.
Thirdly, it is found that the constructed network is sparse through the average
degree and density. Fourthly, it is also demonstrated the degree distributions
of hub nodes and the bottom nodes are the power law and exponential,
respectively. Finally, we prove that clustering coefficient with a definite
value z tends to stabilize at a lower bound as t iterates to a certain number,
and the average distance of G_{t}^{z} has a increasing relationship along with
the value of lnN_{t}.
