  The problem of connectivity assessment in an asymmetric network represented
by a weighted directed graph is investigated in this article. A power iteration
algorithm in a centralized implementation is developed first to compute the
generalized algebraic connectivity of asymmetric networks. After properly
transforming the Laplacian matrix of the network, two sequences of
one-dimensional and two-dimensional subspaces are generated iteratively, one of
which converges to the desired subspace spanned by the eigenvector(s)
associated with the eigenvalue(s) representing the network's generalized
algebraic connectivity. A distributed implementation of the proposed power
iteration algorithm is then developed to compute the generalized algebraic
connectivity from the viewpoint of each node, which is scalable to any
asymmetric network of any size with a fixed message length per node. The
convergence analysis of these algorithms is subsequently provided under some
weak assumptions. The efficiency of the developed algorithms in computing the
network connectivity is then demonstrated by simulations.
