The problem of connectivity assessment of an asymmetric network represented by a weighted directed graph is investigated in this paper. The notion of generalized algebraic connectivity is formulated for this type of network in the context of distributed parameter estimation algorithms. The proposed connectivity measure is then defined in terms of the eigenvalues of the Laplacian matrix of the graph representing the network. A novel distributed algorithm based on the subspace consensus approach is developed to compute the generalized algebraic connectivity from the viewpoint of each node. The Laplacian matrix of the network is properly transformed such that the problem of finding the connectivity measure is reduced to the problem of finding the dominant eigenvalue of an asymmetric matrix. Two sequences of one-dimensional and two-dimensional subspaces are generated iteratively by each node such that either of them converges to the desired subspace spanned by the eigenvectors associated with the desired eigenvalues representing the network connectivity. The effectiveness of the developed algorithm is subsequently demonstrated by simulations.
['Mohammad Mehdi Asadi', 'Mohammad Khosravi', 'Stephane Blouin', 'Amir G. Aghdam']
A subspace consensus approach for distributed connectivity assessment of asymmetric networks