My paper on the bifractality of fractal scale-free networks (FSFNs) is published from Physical Review E.

In this work, we investigated the structures of scale-free networks with fractal property (in which the network diameter follows a power law w.r.t. the number of nodes). In contrast to the small-world networks, fractal networks have large network diameters (or average shortest path lengths) and are typically disassortative in terms of degrees and characterized by the scale invariance, i.e., network properties are preserved under scale transformations. We showed that many FSFNs are structurally bifractal, characterized by two distinct local fractal dimensions; the smaller one corresponding to regions containing the inifinite-degree hub nodes and the larger one corresponding to regions with finite-degree nodes that are infinitely far from the infinite hubs. From our findings, we conjecture that any FSFN is bifractal. This implies that dynamical processes on FSFNs may be influenced by the distinct local fractalities depending on the regions in which the process takes place.

The article can be found here or on arXiv.