This study presents a new approach for complex networks-based analysis of temporal streamflow dynamics. The novelty comes in the form of using nonlinear dynamic concepts to construct the temporal streamflow network. The approach involves three steps. First, the single-variable streamflow time series is represented in a multidimensional phase space using delay embedding, i.e. phase space reconstruction. Next, this reconstructed phase space is treated as a network, with the reconstructed vectors (instead of the streamflow values themselves) serving as the nodes and the connections between them serving as the links. Finally, the strength of each node in the network is determined using a distance metric. The approach is employed independently to monthly streamflow time series observed over a period of 53 years (January 1950-December 2002) from each of 639 stations in the contiguous United States. For each time series, different delay time values for phase space reconstruction are considered and the optimum embedding dimension is determined using the false nearest neighbor (FNN) method. The results indicate the usefulness of the phase space reconstruction-based network construction for examining the temporal connections in streamflow. The distribution of the strengths of nodes for any streamflow network is used to identify the type of the underlying network. The average node strength of each of the 639 streamflow networks are also interpreted: (1) to identify similarities and differences between the stations; (2) to explain the role of catchment and flow properties (drainage area, elevation, and flow mean) on network strength; and (3) to assess the influence of time (i.e. month of the year) on network strength.