  The functional features of spatial networks depend upon a non-trivial
relationship between the topological and physical structure. Here, we explore
that relationship for spatial networks with radial symmetry and disordered
fractal morphology. Under a geometric graphs approach, we quantify the
effectiveness of the exchange of information in the system from center to
perimeter and over the entire network structure. We mainly consider two
paradigmatic models of disordered fractal formation, the Ballistic Aggregation
and Diffusion-Limited Aggregation models, and complementary, the Viscek and
Hexaflake fractals, and Kagome and Hexagonal lattices. First, we show that
complex tree morphologies provide important advantages over regular
configurations, such as an invariant structural cost for different fractal
dimensions. Furthermore, although these systems are known to be scale-free in
space, they have bounded degree distributions for different values of an
euclidean connectivity parameter and, therefore, do not represent ordinary
scale-free networks. Finally, compared to regular structures, fractal trees are
fragile and overall inefficient as expected, however, we show that this
efficiency can become similar to that of a robust hexagonal lattice, at a
similar cost, by just considering a very short euclidean connectivity beyond
first neighbors.
