Characterizing the complexity of time series network graphs: A simplicial approach
We use the techniques of time series network duality to map the time series of the logistic map, at several special parameter values, to equivalent networks using the visibility algorithm. We discuss a set of measures which can analyse the simplicial structure of the resulting networks using the techniques of algebraic topology. We find that the complexity of the simplicial structure and the levels of hierarchy involved increase with the chaoticity of the system. We discuss the implications of our results.