In this paper, we introduce the finite neighboring type and the finite chain length conditions for a connected self-similar set K. We show that with these two conditions, K is a finitely ramified graph directed (f.r.g.d.) fractal defined by Hambly and Nyberg (Proc. Edinb. Math. Soc. (2) 46(1), 1–34 2003). We give some nontrivial examples and compute the harmonic structures on them explicitly. Furthermore, for a f.r.g.d. self-similar set K, we provide an equivalent description, the finitely ramified of finite type (f.r.f.t.) cell structure of K, and investigate the relationship of harmonic structures associated with different f.r.f.t. cell structures of K.

在本文中，我们介绍了一个连接的自相似集K的有限邻近类型和有限链长条件。我们证明在这两个条件下，K是由Hambly和Nyberg定义的有向图（分数）分形图（Proc。Edinb。Math。Soc。（2）46（1），1–34 2003）。我们给出一些非平凡的例子，并明确计算它们的谐波结构。此外，对于frgd自相似组ķ，我们提供了一个等效的描述中，有限的分枝有限型（FRFT）细胞结构的ķ，并调查用的不同分数傅里叶变换单元结构相关联的谐波结构的关系ķ。