Abstract : Connectivity in wireless sensor networks refers to the ability for any two nodes in the network to communicate, which is a prerequisite for nodes to self-organize and form a network. By analyzing the relationship between connectivity and coverage, this paper presents the necessary and sufficient conditions for coverage to imply connectivity. When the node communication radius is greater than or equal to twice the sensing radius, the minimum node coverage set constructed by the genetic algorithm is connected; when the node communication radius is less than twice the sensing radius, a connectivity algorithm based on minimum spanning tree (MST) is introduced to calculate the auxiliary nodes required to ensure the connectivity of the minimum node coverage set constructed by the genetic algorithm, thus guaranteeing the network's coverage and connectivity over the monitored area. Keywords : wireless sensor; network connectivity; coverage set; minimum spanning tree 1. Introduction The minimum coverage set can be selected from a high-density randomly distributed sensor node according to different coverage requirements, but the connectivity between nodes in the minimum coverage set is not considered. That is, under the condition of limited single-node communication radius and monitoring radius, can the smooth network information collection and communication be ensured between different nodes in the selected minimum coverage set? To ensure network connectivity, this paper presents the necessary and sufficient conditions and proofs for node communication radii and monitoring radii to satisfy coverage. When these conditions are not met, auxiliary nodes are constructed using a minimum spanning tree connectivity algorithm to ensure the connectivity of the coverage set. (Full text of "A Wireless Sensor Network Coverage Set Connectivity Algorithm" available for download.)