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Significance This paper highlights that not all scale-free (SF) networks arise through a Barabási−Albert (BA) preferential attachment process. Although evident from the literature, this fact is often overlooked by many researchers. For this purpose, it is demonstrated, with simulations, that established network measures cannot distinguish between BA networks and other SF networks (random-like and lattice-like) with the same degree distribution. Additionally, it is examined whether an existing self-similarity metric is also capable of distinguishing different SF topologies with the same degree distribution. To contribute to this discrimination, this paper introduces a spectral metric, which is shown to be more capable of distinguishing between different SF topologies with the same degree distribution, in comparison with the existing metrics.

Detecting different topologies immanent in scale-free networks with the same degree distribution