Abstract
Network connectivity has been thoroughly investigated in several domains, including physics, neuroscience, and social sciences. This work tackles the possibility of characterizing the topological properties of real-world networks from a quantum-inspired perspective. Starting from the normalized Laplacian of a network, we use a well-defined procedure, based on the dressing transformations, to derive a 1-dimensional Schrödinger-like equation characterized by the same eigenvalues. We investigate the shape and properties of the potential appearing in this equation in simulated small-world and scale-free network ensembles, using measures of fractality. Besides, we employ the proposed framework to compare real-world networks with the Erdős-Rényi, Watts-Strogatz and Barabási-Albert benchmark models. Reconstructed potentials allow to assess to which extent real-world networks approach these models, providing further insight on their formation mechanisms and connectivity properties.
Highlights
Complex network models are an effective and versatile tool to describe the characteristics of complex systems, consisting of a large number of elementary units interacting with each other, and to study the phenomena underlying their dynamics of operation and evolution [1,2,3,4]
The article is organized as follows: in the “Materials and methods” section, we provide a short overview about the Laplacian of a network and the methodology adopted to reconstruct the potential associated with its spectrum; besides, we briefly present the main characteristics of small-world and scale free networks, especially considering the Watts-Strogatz (WS) [33] and the Barabasi-Albert (BA) models [34]
In the “Results and discussion” section, we examine the application of potentials to small-world and scale free networks, we perform a comparison of real-world networks with ensembles of artificial networks, based on potentials
Summary
Complex network models are an effective and versatile tool to describe the characteristics of complex systems, consisting of a large number of elementary units interacting with each other, and to study the phenomena underlying their dynamics of operation and evolution [1,2,3,4].
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