I'm trying to calculate the fractal dimension of a directed (and unweighted) graph by means of the box covering algorithm described in the attached article. I have also found a python implementation of the algorithm (see link below). However, I don't understand if these techniques work only for undirected graphs or if they can be applied to directed graphs as well. Another possibility is to transform my directed graph into an undirected one simply by adding the missing edges (e.g., if there is an edge from node A to node B, I can add the missing edge from B to A, so that the adjacency matrix becomes symmetric and the corresponding graph becomes undirected). I was wondering if the directed graph and its undirected counterpart would have the same fractal dimension. Unfortunately on the internet I cannot find any statemement about the possibility to apply these algorithms to directed graphs.
https://arxiv.org/abs/cond-mat/0701216
http://www-levich.engr.ccny.cuny.edu/~hmakse/modules.py
The box covering algorithm calculates the fractal dimension of a graph. The algorithm is based on the concept of distance between nodes.The distance between nodes can be defined also for directed graphs, so I think the algorithm should work also in tha this case when A box consists of nodes separated by a distance l < lB is possible.
Dear Dr Maharana, many thanks for your answer. Actually I completely agree with you. I also tried to run the attached python code and it does not complain at all when I try to use directed graphs.
I offer an alternative index to measure or quantify fractal structure of graph. It is ht-index, as developed in this paper:
https://www.researchgate.net/publication/236627484_Ht-Index_for_Quantifying_the_Fractal_or_Scaling_Structure_of_Geographic_Features
It leads to the third definition of fractal:
https://www.researchgate.net/publication/309428627_The_third_definition_of_fractal
Article Ht-Index for Quantifying the Fractal or Scaling Structure of...
Presentation The third definition of fractal
Dear Dr. Jiang, many thanks for your answer. I'm reading your links carefully, trying to apply your definition of fractal to the adjacency matrices of random networks.
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