  In this work, inspired by secret sharing schemes, we introduce a
privacy-preserving approach for network consensus, by which all nodes in a
network can reach an agreement on their states without exposing the individual
state to neighbors. With the privacy degree defined for the agents, the
proposed method makes the network resistant to the collusion of any given
number of neighbors, and protects the consensus procedure from communication
eavesdropping. Unlike existing works, the proposed privacy-preserving algorithm
is resilient to node failures. When a node fails, the method offers the
possibility of rebuilding the lost node via the information kept in its
neighbors, even though none of the neighbors knows the exact state of the
failing node. Moreover, it is shown that the proposed method can achieve
consensus and average consensus almost surely, when the agents have arbitrary
privacy degrees and a common privacy degree, respectively. To illustrate the
theory, two numerical examples are presented.
