  In a multi-agent system, agents coordinate to achieve global tasks through
local communications. Coordination usually requires sufficient information
flow, which is usually depicted by the connectivity of the communication
network. In a networked system, removal of some agents may cause a
disconnection. In order to maintain connectivity in agent removal, one can
design a robust network topology that tolerates a finite number of agent
losses, and/or develop a control strategy that recovers connectivity. This
paper proposes a decentralized control scheme based on a sequence of
replacements, each of which occurs between an agent and one of its immediate
neighbors. The replacements always end with an agent, whose relocation does not
cause a disconnection. We show that such an agent can be reached by a local
rule utilizing only some local information available in agents' immediate
neighborhoods. As such, the proposed message passing strategy guarantees the
connectivity maintenance in arbitrary agent removal. Furthermore, we
significantly improve the optimality of the proposed scheme by incorporating
$\delta$-criticality (i.e. the criticality of an agent in its
$\delta$-neighborhood).
