  Random networks of symmetrically coupled, excitable elements can
self-organize into coherently oscillating states if the networks contain loops
(indeed loops are abundant in random networks) and if the initial conditions
are sufficiently random. In the oscillating state, signals propagate in a
single direction and one or a few network loops are selected as driving loops
in which the excitation circulates periodically. We analyze the mechanism,
describe the oscillating states, identify the pacemaker loops and explain key
features of their distribution. This mechanism may play a role in epileptic
seizures.
