For over a decade, the Nash Bargaining Solution (NBS) concept from cooperative game theory has been used in networks to share resources fairly. Due to its many appealing properties, it has recently been used for assigning bandwidth in a general topology network between applications that have linear utility functions. In this paper, we use this concept for allocating the bandwidth between applications with general concave utilities. Our framework includes in fact several other fairness criteria, such as the max-min criteria. We study the impact of concavity on the allocation and present computational methods for obtaining fair allocations in a general topology, based on a dual Lagrangian approach and on Semi-Definite Programming.