We analyze in situ measurements of the solar wind velocity obtained by the Advanced Composition Explorer (ACE) and the Helios spacecraft during the years 1998 – 2012 and 1975 – 1983, respectively. The data mainly belong to solar cycles 23 (1996 – 2008) and 21 (1976 – 1986). We used the directed horizontal-visibility-graph (DHVg) algorithm and estimated a graph functional, namely, the degree distance (D), which is defined using the Kullback–Leibler divergence (KLD) to understand the time irreversibility of solar wind time-series. We estimated this degree-distance irreversibility parameter for these time-series at different phases of the solar activity cycle. The irreversibility parameter was first established for known dynamical data and was then applied to solar wind velocity time-series. It is observed that irreversibility in solar wind velocity fluctuations show a similar behavior at 0.3 AU (Helios data) and 1 AU (ACE data). Moreover, the fluctuations change over the phases of the activity cycle.