Recurrence networks are important statistical tools used for the analysis of time series data with several practical applications. Though these networks are complex and characterize objects with structural scale invariance, their properties from a complex network perspective have not been fully understood. In this Letter, we argue, with numerical support, that the recurrence networks from chaotic attractors with continuous measure can neither show scale free topology nor small world property. However, if the critical threshold is increased from its optimum value, the recurrence network initially crosses over to a complex network with the small world property and finally to the classical random graph as the threshold approaches the size of the strange attractor.