  In this paper we investigate the problem of the sudden disconnection of an
edge in a discrete-time multi-agent consensus network. If the graph remains
strongly connected, the multi-agent system still achieves consensus, but in
general, unless the information exchange between each pair of agents is
symmetric, the agents' states converge to a drifted value of the original
consensus value. Consequently the edge disconnection can go unnoticed. In this
paper the problems of detecting an edge disconnection and of identifying in a
finite number of steps the exact edge that got disconnected are investigated.
Necessary and sufficient conditions for both problems to be solvable are
presented, both in case all the agents' states are available and in case only a
subset of the agents' states is measured. Finally, an example of a network of 7
agents is provided, to illustrate some of the theoretical results derived in
the paper.
