title: Phase transition in the parametric natural visibility graph.
abstract: We investigate time series by mapping them to the complex networks using a parametric natural visibility graph (PNVG) algorithm that generates graphs depending on arbitrary continuous parameter-the angle of view. We study the behavior of the relative number of clusters in PNVG near the critical value of the angle of view. Artificial and experimental time series of different nature are used for numerical PNVG investigations to find critical exponents above and below the critical point as well as the exponent in the finite size scaling regime. Altogether, they allow us to find the critical exponent of the correlation length for PNVG. The set of calculated critical exponents satisfies the basic Widom relation. The PNVG is found to demonstrate scaling behavior. Our results reveal the similarity between the behavior of the relative number of clusters in PNVG and the order parameter in the second-order phase transitions theory. We show that the PNVG is another example of a system (in addition to magnetic, percolation, superconductivity, etc.) with observed second-order phase transition.
authors.affiliation: National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kiev 03056, Ukraine.|Institute for Information Recording, NAS Ukraine, Kiev 03113, Ukraine.
authors.forename: A A
authors.initials: AA
authors.lastname: Snarskii
authors.affiliation: JSC Nauka-Service, Moscow 127473, Russia.
authors.forename: I V
authors.initials: IV
authors.lastname: Bezsudnov