On 04/24/2014 12:32 AM, Xiaohu Hu wrote:
Hi all,
I would like to determine the fractal dimension of the graph. I can assigned a "geometric distance" between each pair of vertices, therefore, I could also assign each edge a "length". One thing I could do is to somehow define a center and then count the the number of the nodes within "a circle" with increasing "radius". See how the number of the vertices scales with the increasing radius.
I wonder Is there any other ways to calculate the fractal dimension using some features from any graph-tool functions? Can I estimate the fractal dimension from the adjacency matrix maybe? I would appreciate any advise.
There are no implementations of fractal dimension in graph-tool. Note that this is an active area of research, and there is no universally accepted definition of a generalized fractal dimension for graphs. I think the most famous method is: http://www.nature.com/nature/journal/v433/n7024/abs/nature03248.html But there are several issues with this approach. See e.g. the following paper for a well-founded criticism: http://journals.aps.org/pre/pdf/10.1103/PhysRevE.84.066111 Best, Tiago -- Tiago de Paula Peixoto <tiago@skewed.de>