  In this paper we consider a dynamic version of the Erd\H{o}s-R\'{e}nyi random
graph, in which edges independently appear and disappear in time, with the on-
and off times being exponentially distributed. The focus lies on the evolution
of the principle eigenvalue of the adjacency matrix in the regime that the
number of vertices grows large. The main result is a functional central limit
theorem, which displays that the principal eigenvalue essentially inherits the
characteristics of the dynamics of the individual edges.
