Abstract In this paper, we propose a novel node importance evaluation method from the perspective of the existence of mutual dependence among nodes. The node importance comprises its initial importance and the importance contributions from both the adjacent and non-adjacent nodes according to the dependence strength between them. From the simulation analyses on an example network and the ARPA network, we observe that our method can well identify the node importance. Then, the cascading failures on the Netscience and E-mail networks demonstrate that the networks are more vulnerable when continuously removing the important nodes identified by our method, which further proves the accuracy of our method.