  We study a stochastic compartmental susceptible-infected (SI) epidemic
process on a configuration model random graph with a given degree distribution
over a finite time interval $[0,T],$ for some $ T>0$. In this setting, we split
the population of graph nodes into two compartments, namely, $S$ and $I$,
denoting the susceptible and infected nodes, respectively. In addition to the
sizes of these two compartments, we study counts of $SI$-edges (those
connecting a susceptible and an infected node) and $SS$-edges (those connecting
two susceptible nodes). We describe the dynamical process in terms of these
counts and present a functional central limit theorem (FCLT) for them, a
scaling limit of the dynamical process as $n$, the number of nodes in the
random graph, grows to infinity. To be precise, we show that these counts, when
appropriately scaled, converge weakly to a continuous Gaussian vector
martingale process the usual Skorohod space of real 3-dimensional vector-valued
\cadlag\, functions on $[0,T]$ endowed with the Skorohod topology. We assume
certain technical requirements for this purpose. We discuss applications of our
FCLT in percolation theory (from a non-equilibrium statistical mechanics point
of view), and in computer science in the context of spread of computer viruses.
We also provide simulation results for some common degree distributions.
