Netons: Vibrations of Complex Networks

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 $r=1$.

9 pages, 6 figures, to appear in JPA

References in corpus (8)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• Evolution of networks
• Mean-field theory for scale-free random networks
• Synchronization on small-world networks
• Spectra and eigenvectors of scale-free networks
• Diffusion, localization and dispersion relations on ``small-world'' lattices
• Phase ordering on small-world networks with nearest-neighbor edges

Cited by in corpus (6)

• The Physics of Communicability in Complex Networks
• A Vibrational Approach to Node Centrality and Vulnerability in Complex Networks
• Quantum and classical diffusion in small-world networks
• Phase Transition of XY Model in Heptagonal Lattice
• Electron in a tangled chain: multifractality at the small-world critical point
• Eigenvector localization as a tool to study small communities in online social networks