Many of the behaviors observed in actual systems are comparable to
scale-free and small world structures in network research. In contrast
to conventional hierarchical networks, the unusual fractal hierarchical
network we created in this research has a pyramidal structure. The
findings we get from this network are expanded to be applicable to
arbitrary hierarchical networks. The average path length of unweighted
and weighted hierarchical networks are the main topics of this paper. We
demonstrate that, in the unweighted case, when the number of iterations
z tends to infinity, the average path length is only related to the
number of blocks of the hierarchical network. Additionally, in the
weighted network, the average path length is related to the number of
blocks r and the weighting factor w of the hierarchical network.