In this paper, an algorithm that forms a dynamic and self-organizing network is demonstrated. The hypothesis of this work is that in order to achieve a resilient and adaptive peer-to-peer (P2P) network, each network node must proactively maintain a minimum number of edges. Specifically, low-level communication protocols are not sufficient by themselves to achieve high-service availability, especially in the case of ad hoc or dynamic networks with a high degree of node addition and deletion. The concept has been evaluated within a P2P agent application in which each agent has a goal to maintain a preferred number of connections to a number of service providing agents. Using this algorithm, the agents update a weight value associated with each connection, based on the perceived utility of the connection to the corresponding agent. This utility function can be a combination of several node or edge parameters, such as degree k of the target node, or frequency of the message response from the node. This weight is updated using a set of Hebbian-style learning rules, such that the network as a whole exhibits adaptive self-organizing behavior. The principal result is the finding that by limiting the connection neighborhood within the overlay topology, the resulting P2P network can be made highly resilient to targeted attacks on high-degree nodes, while maintaining search efficiency.