  We study the problem of leader election among mobile agents operating in an
arbitrary network modeled as an undirected graph. Nodes of the network are
unlabeled and all agents are identical. Hence the only way to elect a leader
among agents is by exploiting asymmetries in their initial positions in the
graph. Agents do not know the graph or their positions in it, hence they must
gain this knowledge by navigating in the graph and share it with other agents
to accomplish leader election. This can be done using meetings of agents, which
is difficult because of their asynchronous nature: an adversary has total
control over the speed of agents. When can a leader be elected in this
adversarial scenario and how to do it? We give a complete answer to this
question by characterizing all initial configurations for which leader election
is possible and by constructing an algorithm that accomplishes leader election
for all configurations for which this can be done.
