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According to this article from Wikipedia, the box-covering algorithm calculates the fractal dimension of a graph. The algorithm is based on the concept of distance between nodes; see for example the sentence:

A box consists of nodes separated by a distance $l < l_B$.

The distance between nodes can be defined also for directed graphs, so I think the algorithm should work also in that case. However, on the Internet, I cannot find any explicit statement about the possibility to use this algorithm for directed graphs.

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The algorithm in question does not impose any constraints on the graphs it can be applied to, so it plainly does not care how whether your graph is directed or not.

However, when applying the algorithm to directed graph, you imply a definition of dimension (which also depend on how exactly you adapt it to directed graphs). The more crucial question is whether this algorithm makes any sense for your application. Unfortunately, only you can answer that question.

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  • $\begingroup$ Many thanks for your answer. Could you please explain what you mean when you say that the more crucial question is whether the algorithm makes any sense for my application? Do you think there may be other ways for measuring graph fractality? $\endgroup$
    – user2983638
    Nov 30 '16 at 16:16
  • $\begingroup$ @user2983638: Typically, you do not want to obtain a measure for its own sake but to interpret it with respect to the organisation, robustness, or similar of your network. These interpretations depend on the definition of your measure and whether this makes any sense for your network, what direction means in your network, and so on. For some applications, it may be valid to treat a measure as a blackbox, but even then you usually want to assure that you are not measuring some trivial effect – which would be determined by your a-priori knowledge about the network. $\endgroup$
    – Wrzlprmft
    Nov 30 '16 at 16:23

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