Hierarchical networks as fundamental models to describe the complex networks, have many applications in networks science, engineering technology and so on. In this paper, we first propose a new class of hierarchical networks with fractal structure, which are the networks with triangles compared to traditional hierarchical networks. Second, we study the precise results of some structural properties to derive small-world effect and scale-free feature. Third, it is found that the constructed network is sparse through the average degree and density. Fourth, it is also demonstrated that 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 an increasing relationship along with the value of $ln{N}_t$.

层次网络作为描述复杂网络的基础模型，在网络科学、工程技术等领域有着广泛的应用。在本文中，我们首先提出了一类新的具有分形结构的层次网络，它是与传统层次网络相比具有三角形的网络。其次，我们研究了一些结构特性的精确结果，以得出小世界效应和无标度特征。第三，通过平均度和密度发现构建的网络是稀疏的。第四，还证明了中心节点和底层节点的度分布分别是幂律和指数分布。最后，我们证明了具有确定值的聚类系数$z$趋于稳定在下限，因为$吨$迭代到一定次数，平均距离为$G_{吨}^z$与价值的关系越来越大$ln{ñ}_{吨}$.