Abstract: Aiming at the threshold collusion and probabilistic connectivity problems in the process of wireless sensor network (WSN) key pre-distribution, an scheme based on matrix eigenvector (EBSC) is proposed. By using a generating matrix A, 2N secret matrices can be dynamically generated according to the different types of application nodes. The problem of threshold collusion in classical BLOM scheme and probabilistic connectivity in probabilistic is sloved. Full connectivity of WSN network (that is, any two nodes in the network can communicate directly) can be realized. Moreover, utilizing the properties of eigenvalues and eigenvectors in the EBSC scheme, a single authentication is used in the application of nodes, which greatly improves the security performance of the network. The comparison analysis shows that the new scheme has advantages in node storage, computation and network communication energy consumption. Especially, in the case of large network updates, the new scheme can realize the whole network updates of scale N by simple assignment operation and lightweight communication consumption, avoiding complex matrix expansion operation. This shows that EBSC algorithm is more suitable for energy-constrained WSN networks.