Scale-free networks as an epiphenomenon of memory

A local model of preferential attachment with short-term memory generates scale-free networks, which can be readily computed by memristors.

EPL 109, 2 (2015)

F. Caravelli, A. Hamma, M. Ventra

Scale-free networks as an epiphenomenon of memory

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.

More in Remembering to learn

  • EPL

    Memristive networks

    A simple solvable model of memristive networks suggests a correspondence between the asymptotic states of memristors and the Ising model.

  • European Physical Journal B

    Solvable memristive circuits

    Exact solutions for the dynamics of interacting memristors predict whether they relax to higher or lower resistance states given random initialisations.

  • International Journal of Parallel, Emergent and Distributed Systems

    Memristive networks and learning

    Memristive networks preserve memory and have the ability to learn according to analysis of the network’s internal memory dynamics.

  • Physical Review E

    Dynamics of memristors

    Exact equations of motion provide an analytical description of the evolution and relaxation properties of complex memristive circuits.