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Recently, benefiting from rapid development of energy harvesting technologies, the research trend of wireless sensor networks has shifted from the battery-powered network to the one that can harvest energy from ambient environments. In such networks, a proper use of harvested energy poses plenty of challenges caused by numerous influence factors and complex application environments. Although numerous works have been based on the energy status of sensor nodes, no work refers to the issue of minimizing the overall data transmission cost by adjusting transmission power of nodes in energy-harvesting wireless sensor networks. In this paper, we consider the optimization problem of deriving the energy-neutral minimum cost paths between the source nodes and the sink node. By introducing the concept of energy-neutral operation, we first propose a polynomial-time optimal algorithm for finding the optimal path from a single source to the sink by adjusting the transmission powers. Based on the work earlier, another polynomial-time algorithm is further proposed for finding the approximated optimal paths from multiple sources to the sink node. Also, we analyze the network capacity and present a near-optimal algorithm based on the Ford-Fulkerson algorithm for approaching the maximum flow in the given network. We have validated our algorithms by various numerical results in terms of path capacity, least energy of nodes, energy ratio, and path cost. Simulation results show that the proposed algorithms achieve significant performance enhancements over existing schemes. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]