  Average consensus algorithms compute the global average of sensor data in a
distributed fashion using local sensor nodes. Simple execution, decentralized
philosophy make these algorithms suitable for WSN scenarios. Most of the
researchers have studied the average consensus algorithms by modeling the
network as an undirected graph. But, WSNs in practice consist of asymmetric
links and the undirected graph cannot model the asymmetric links. Therefore,
these studies fail to study the actual performance of consensus algorithms on
WSNs. In this paper, we model the WSN as a directed graph and derive the
explicit formulas of the ring, torus, $r$-nearest neighbor ring, and
$m$-dimensional torus networks. Numerical results subsequently demonstrate the
accuracy of directed graph modeling. Further, we study the effect of asymmetric
links, the number of nodes, network dimension, and node overhead on the
convergence rate of average consensus algorithms.
