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

Area of Science:

• Network Science
• Graph Theory
• Statistical Physics

Background:

• Scale-free (SF) networks exhibit power-law (PL) degree distributions, a key characteristic in complex systems.
• The Barabási-Albert (BA) model is a common mechanism for generating SF networks via preferential attachment.
• However, not all networks with PL degree distributions are generated by the BA process, a nuance often overlooked.

Purpose of the Study:

• To demonstrate that established network topology measures are insufficient to differentiate BA networks from other SF networks with identical degree distributions.
• To evaluate the efficacy of a self-similarity metric in distinguishing SF network topologies with the same degree distribution.
• To introduce a novel spectral metric for improved discrimination between SF network topologies.

Main Methods:

• Simulations were conducted to analyze network topology measures.
• An existing self-similarity metric was assessed for its discriminatory power.
• A new spectral metric was developed and compared against existing methods.

Main Results:

• Established topological measures failed to distinguish between BA and other SF network types (random-like, lattice-like) sharing the same degree distribution.
• The existing self-similarity metric also showed limitations in differentiating these topologies.
• The newly introduced spectral metric demonstrated superior capability in distinguishing between different SF topologies with identical degree distributions.

Conclusions:

• Network topology analysis requires more sophisticated metrics beyond standard measures and self-similarity to differentiate SF network generation processes.
• The proposed spectral metric offers a more effective tool for identifying the underlying structure of scale-free networks.
• This research clarifies the diversity of mechanisms leading to scale-free properties in complex networks.