  We give exact relations for certain types of the hierarchic fractal
structures. In the blatant distinction from regular networks of the "small
world" (SW) topology [1], regular fractal networks manifests the logarithmic
dependence of the characteristic path length on number of vertices N which is
typically just for random networks. Due to this fact, for the hierarchic
networks there is no effect of an abrupt drop of the mean path length caused by
the introduction into a regular structure only a few random edges. The
clustering coefficient of the hierarchic structures is equal zero and in a
process of randomization it slightly grows up to the random networks value k/N,
where k is mean number of the nearest neighbors, in vivid contrast with the
small world networks behavior. We considered also the problem of unification of
two isolated SW and Caley tree networks in the limits of weak (through one
point) and strong (many points) connection and deduced a specific algebra for
the mean path length of the unified network in terms of the isolated networks
path lengths. The sewing together of the tree-like networks may be performed in
the one-bottom point or in the crown top to crown top manners. In such a way we
come to the concept of bi-trees of two types having different topologies. We
demonstrated the difference between two possible probabilistic models of
introducing randomness: the model with substitution of a certain number of cut
off links of the regular lattice by the equal number of edges stochastically
distributed over the lattice (totally random model) and the artillery model,
when one end of the broken link remains connected with the origin lattice.
