Is there any chance that a fractal can be used for graph visualization?

Question

It is certainly possible to create a mapping between hierarchies and some of the fractals:

• http://davis.wpi.edu/~matt/courses/fractals/trees.html

According to wikipedia it is possible to deviate from the original fractal formula: https://en.wikipedia.org/wiki/Finite_subdivision_rule , so my (not so) educated guess would be that it is possible to write subdivision rules to display any kind of hierarchical data.

By some of the non-hierarchical graphs we are lucky, since we can use clustering to make them more or less hierarchical and we can probably use the same rule inside the clusters: https://en.wikipedia.org/wiki/Scale-free_network#Hierarchical_network_model

So my question is: Is it possible in theory to use fractals or subdivision rules to display random network data (which I guess cannot be clustered efficiently)?

Answer 1

I found an interesting article which answers my question.

Fractal and Transfractal Scale-Free Networks

• Hernán D. Rozenfeld, Lazaros K. Gallos, Chaoming Song, Hernán A. Makse
• https://arxiv.org/pdf/0808.2206v1.pdf

The answer depends on whether a scale-free network is homogeneous. Homogeneous scale free networks are self-similar, so we can do a mapping between a fractal and the network and so visualize the network. By inhomogeneous networks I am not sure, subdivision rules might help in some cases, but certainly not in all of them, so we need probably a more traditional way to visualize such network graphs.