  We consider the problem of average consensus in a distributed system
comprising a set of nodes that can exchange information among themselves. We
focus on a class of algorithms for solving such a problem whereby each node
maintains a state and updates it iteratively as a linear combination of the
states maintained by its in-neighbors, i.e., nodes from which it receives
information directly. Averaging algorithms within this class can be thought of
as discrete-time linear time-varying systems without external driving inputs
and whose state matrix is column stochastic. As a result, the algorithms
exhibit a global invariance property in that the sum of the state variables
remains constant at all times. In this paper, we report on another invariance
property for the aforementioned class of averaging algorithms. This property is
local to each node and reflects the conservation of certain quantities
capturing an aggregate of all the values received by a node from its
in-neighbors and all the values sent by said node to its out-neighbors (i.e.,
nodes to which it sends information directly) throughout the execution of the
averaging algorithm. We show how this newly-discovered invariant can be
leveraged for detecting errors while executing the averaging algorithm.
