We analyze consensus algorithms in networks of multi-agents with time-varying
topologies and delays. The topology is modeled as induced by a homogeneous
Markov chain and is rather general, including the
independent-identical-distribution (i.i.d.) topology process, asynchronous
consensus algorithms, and the random waypoint model of mobile agents. We prove
that, for networks with self-links but without transmission delays, consensus
can be reached if the union graph across a finite time interval has positive
probability of having a spanning tree and this situation is repeatable.