  We observe the actions of a $K$ sub-sample of $N$ individuals up to time $t$
for some large $K<N$. We model the relationships of individuals by i.i.d.
Bernoulli($p$)-random variables, where $p\in (0,1]$ is an unknown parameter.
The rate of action of each individual depends on some unknown parameter $\mu>
0$ and on the sum of some function $\phi$ of the ages of the actions of the
individuals which influence him. The function $\phi$ is unknown but we assume
it rapidly decays. The aim of this paper is to estimate the parameter $p$
asymptotically as $N\to \infty$, $K\to \infty$, and $t\to \infty$. Let $m_t$ be
the average number of actions per individual up to time $t$. In the subcritical
case, where $m_t$ increases linearly, we build an estimator of $p$ with the
rate of convergence
$\frac{1}{\sqrt{K}}+\frac{N}{m_t\sqrt{K}}+\frac{N}{K\sqrt{m_t}}$. In the
supercritical case, where $m_{t}$ increases exponentially fast, we build an
estimator of $p$ with the rate of convergence
$\frac{1}{\sqrt{K}}+\frac{N}{m_{t}\sqrt{K}}$.
