An electrostatics method for converting a time-series into a weighted complex network

This paper proposes a new method for converting a time-series into a weighted graph (complex network), which builds on electrostatics in physics. The proposed method conceptualizes a time-series as a series of stationary, electrically charged particles, on which Coulomb-like forces can be computed. This allows generating electrostatic-like graphs associated with time-series that, additionally to the existing transformations, can be also weighted and sometimes disconnected. Within this context, this paper examines the structural similarity between five different types of time-series and their associated graphs that are generated by the proposed algorithm and the visibility graph, which is currently the most popular algorithm in the literature. The analysis compares the source (original) time-series with the node-series generated by network measures (that are arranged into the node-ordering of the source time-series), in terms of a linear trend, chaotic behaviour, stationarity, periodicity, and cyclical structure. It is shown that the proposed electrostatic graph algorithm generates graphs with node-measures that are more representative of the structure of the source time-series than the visibility graph. This makes the proposed algorithm more natural rather than algebraic, in comparison with existing physics-defined methods. The overall approach also suggests a methodological framework for evaluating the structural relevance between the source time-series and their associated graphs produced by any possible transformation.