Netons: Vibrations of Complex Networks

TL;DR

This paper studies vibrational modes called netons in complex networks, revealing how network topology influences their spectral properties, including the presence of energy gaps and differences between small-world and scale-free networks.

Contribution

It introduces the concept of netons in complex networks and compares vibrational spectra across different network models, highlighting topological effects on rigidity and excitability.

Findings

A finite energy gap appears in the density of neton levels.

Small-world networks show an additional peak in level density.

Scale-free networks exhibit a power-law tail indicating high-energy excitability.

Abstract

We consider atoms interacting each other through the topological structure of a complex network and investigate lattice vibrations of the system, the quanta of which we call {\em netons} for convenience. The density of neton levels, obtained numerically, reveals that unlike a local regular lattice, the system develops a gap of a finite width, manifesting extreme rigidity of the network structure at low energies. Two different network models, the small-world network and the scale-free network, are compared: The characteristic structure of the former is described by an additional peak in the level density whereas a power-law tail is observed in the latter, indicating excitability of netons at arbitrarily high energies. The gap width is also found to vanish in the small-world network when the connection range $r = 1$.