We report the results of studies of improved tests for non-linearity based on time series-induced network statistics and surrogate data.We compare results from the network-based statistics with the earlier tests available in the literature and demonstrate the superiority of these tests over the previous tests for several systems. The method we propose is based on constructing a network from a time series and using easily computable parameters of the resulting network such as the average path length, graph density and clustering coefficient as test statistics for the surrogate data test. These statistics are tested for their ability to distinguish between nonlinear processes and linear noise processes, using surrogate data tests on time series obtained from the Rössler system, the Lorenz system,the Henon map, the logistic map and an actual experimental time series of wind speed data, and compared with popularly used time series associated statistics. The network-based statistics are found to distinguish between the nonlinear time series and surrogates derived from the data to a higher degree than the commonly used time series based statistics, even in the presence of measurement noise and dynamical noise. These statistics may thus prove tobe of value in distinguishing between time series derived from nonlinear processes and time series obtained from linearly correlated stochastic processes even in the presence of measurement noise and dynamical noise. The results also show that the efficiency of the network parameters is not exacerbated by the presence of outliers in the given time series.