  This article is concerned with the asymptotic behaviour of random vectors in
a diluted ferromagnetic model. We consider a model introduced by Bovier &
Gayrard (1993) with ferromagnetic interactions on a directed Erd\H{o}s-R\'enyi
random graph. Here, directed connections between graph nodes are uniformly
drawn at random with a probability p that depends on the number of nodes N and
is allowed to go to zero in the limit. If $Np\longrightarrow\infty$ in this
model, Bovier & Gayrard (1993) proved a law of large numbers almost surely, and
Kabluchko et al. (2020) proved central limit theorems in probability. Here, we
generalise these results for $\beta<1$ in the regime $Np\longrightarrow\infty$.
We show that all those random vectors on the spin configuration that have a
limiting distribution under the Curie-Weiss model converge weakly towards the
same distribution under the diluted model, in probability on graph
realisations. This generalises various results from the Curie-Weiss model to
the diluted model. As a special case, we derive a law of large numbers and
central limit theorem for two disjoint groups of spins.
