Towards fractal origins of the community structure in complex networks: a model-based approach

In this paper, we pose a hypothesis that the structure of communities in complex networks may result from their latent fractal properties. This hypothesis is based not only on the general observation that many real networks have multilevel organization, which is reminiscent of the geometric self-similarity of classical fractals. Quantitative arguments supporting this hypothesis are: first, many non-fractal real complex networks that have a well-defined community structure reveal fractal properties when suitably diluted; second, the scale-free community size distributions observed in many real networks directly relate to scale-invariant box mass distributions, which have recently been described as a fundamental feature of fractal complex networks. We test this hypothesis in a general model of evolving network with community structure that exhibits dual scale invariance: at the level of node degrees and community sizes, respectively. We show that, at least in this model, the proposed hypothesis cannot be rejected. The argument for this is that a kind of fractal core can be identified in the networks studied, which appears as a macroscopic connected component when the edges between modules identified by the community detection algorithm are removed in a supervised manner.