  Some features of random networks with excitable nodes that are embeddable in
the Euclidean space are not describable in terms of the conventional integrate
and fire model (IFM) alone, and some further details should be involved. In the
present paper we consider the effect of the retardation, i.e. the time that is
needed for a signal to traverse between two agents. This effect becomes
important to discover the differences between e.g. the neural networks with low
and fast axon conduct times. We show that the inclusion of the retardation
effects makes some important changes in the statistical properties of the
system. It considerably suppresses/restricts the amplitude of the possible
oscillations in the random network. Additionally, it causes the critical
exponents in the critical regime to considerably change.
