In the Dynamic Rechargeable Networks (DRNs), to maximize the throughput by efficient energy allocation, the existing studies usually consider the spatio-temporal dynamic factors of the harvested energy, and seldom the network dynamic factors simultaneously, such as the time variable network resources and wireless interference. To take the network dynamic factors together, this paper studies the quite challenging problem, the network throughput maximization in the DRNs. We introduce the Time-Expanded Graph (TEG) to describe the above dynamic factors in an obvious way and design the Single Pair Throughput maximization (SPT) algorithm based on TEG. In the case of multiple pairs of source-targets, this paper introduces the Garg and Könemann's framework and then designs the Multiple Pairs Throughput (MPT) algorithm to maximize the overall throughput of all pairs. To reduce the time complexity, this paper proposes a Distributed and Parallel Throughput algorithm (DPT). In real applications, the network dynamic factors may not be known in advance. This paper proposes an Online Time-Span Algorithm (OTA) with Markov approximation and Lyapunov optimization, and conducts the extensive numerical evaluation based on the simulated data and the data collected by our real system. The numerical simulation results demonstrate the throughput improvement of our algorithms.