Scale-free networks as an epiphenomenon of memory

Abstract

Many realistic networks are scale-free, with small characteristic path lengths, high clustering, and power law in their degree distribution. They can be obtained by dynamical networks in which a preferential attachment process takes place. However, this mechanism is non-local, in the sense that it requires knowledge of the whole graph in order for the graph to be updated. Instead, if preferential attachment and realistic networks occur in physical systems, these features need to emerge from a local model. In this paper, we propose a local model and show that a possible ingredient (which is often underrated) for obtaining scale-free networks with local rules is memory. Such a model can be realised in solid-state circuits, using non-linear passive elements with memory such as memristors, and thus can be tested experimentally.

6 pages+3 supplementary; 11 figures; typos corrected, text clarified and new numerical and analytical results added; accepted in EPL

References in corpus (5)

• Emergent complex neural dynamics
• Memory effects in complex materials and nanoscale systems
• Scale-Free Networks Generated By Random Walkers
• Scale Free Networks from Self-Organisation
• Master-equation analysis of accelerating networks

Cited by in corpus (10)

• Memcomputing: Leveraging memory and physics to compute efficiently
• The complex dynamics of memristive circuits: analytical results and universal slow relaxation
• Locality of interactions for planar memristive circuits
• Asymptotic behavior of memristive circuits
• Memristive Networks: from Graph Theory to Statistical Physics
• The mise en scene of memristive networks: effective memory, dynamics and learning
• A mean-field model of memristive circuit interaction
• Memory-induced long-range order in dynamical systems
• A phase transition creates the geometry of the continuum from discrete space
• "Spectrally gapped" random walks on networks: a Mean First Passage Time formula