Many schemes have been examined in the recent past in order to define a methodology for efficient resource sharing in combination with the temporal characteristics of dynamically varying topologies whereas others create a ground for a combination of temporal and spatial techniques. This chapter provides a brief introduction to, and motivation for, topology formation for P2P network connectivity and configuration from a network resource availability viewpoint. Efficient topology formation is probably the crucial parameter for enabling end-to-end reliability and data integrity between peers. The research background is presented using different approaches in the field of topology formation with respect to the parameters that affect the reliability issues of each node. Self-awareness is presented as well as the choice of mechanisms for efficient and reliable communication in a dynamically changing peer-to-peer system. Thereafter the recent adaptive heuristic-based P2P network connectivity approach for topology configuration for resource availability is presented along with some conducted results extracted from the research bibliography. Finally the chapter ends with the conclusion based on the general discussion of the covered issues in the chapter and the open ended research issues that come along with the discussed ones.