Time series-networks are network representations of time series from dynamical systems. They allow investigation of a given system using complex network techniques. Such investigations have been carried out in the past, for example in [1-3]. These studies have attempted to characterize given time series using standard network metrics. In our study, we consider the derived time series-network as a simplicial structure . This allows us to look at the time series-network at different complexity levels. We carry out our analysis using logistic map time series, as it is a very well known system.