Asymptotic versus mesoscopic spectral dimensions in networks and inhomogeneous structures

Abstract

"Every object that biology studies is a system of systems." (François Jacob, 1974). Most networks feature intricate architectures originating from tinkering, a repetitive use of existing components where structures are not invented but reshaped. Linking the properties of primitive components to the emergent behavior of composite networks remains a key open challenge. Here, we show that modular compositions generically decouple the spectral and Fiedler dimensions, so that networks with identical thermodynamic exponents can exhibit parametrically different equilibration dynamics.

arXiv comment5 pages, 3 figures and Supplementary Information

References in corpus (18)

• Synchronization in small-world systems
• Random walks on graphs: ideas, techniques and results
• Spectral entropies as information-theoretic tools for complex network comparison
• Bose-Einstein Condensation on inhomogeneous complex networks
• Bose-Einstein condensation in inhomogeneous Josephson arrays
• Evolution of a Modular Software Network
• Laplacian paths in complex networks: information core emerges from entropic transitions
• Bose-Einstein Condensation on inhomogeneous networks: mesoscopic aspects versus thermodynamic limit
• Phase-ordering kinetics on graphs
• Geometrical universality in vibrational dynamics
• Anomalous diffusion and response in branched systems: a simple analysis
• Topological Effects caused by the Fractal Substrate on the Nonequilibrium Critical Behavior of the Ising Magnet
• Critical behaviour of the Rouse model for gelling polymers
• Evolution in the Debian GNU/Linux software network: analogies and differences with gene regulatory networks
• Networks with many structural scales: a Renormalization Group perspective
• Multi-scale Laplacian community detection in heterogeneous networks
• Strange Attractors in Complex Networks
• Probing the local structure: macromolecular combs in external fields