Scale-free networks as an epiphenomenon of memory

¹ Department of Computer Science, University College London - Gower Street, London WC1E 6BT, UK
² Invenia Technical Computing - 135 Innovation Dr., Winnipeg, MB R3T 6A8, Canada
³ London Institute of Mathematical Sciences - 35a South Street, London W1K 2XF, UK
⁴ Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University Beijing 100084, PRC
⁵ Department of Physics, University of California-San Diego - La Jolla, CA 92093, USA

Received: 24 September 2014
Accepted: 14 January 2015

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.