We observe the actions of a K sub-sample of N individuals until time t for some large K smaller than N.
We do not know if the individuals i and j are connected or not. We model their relationships by i.i.d. Bernoulli(p)-random variables, where p in (0,1] is an unknown parameter. Each individual acts autonomously at some unknown rate \mu> 0 and acts by mimetism at some rate proportional to the sum of some function \phi of the ages of the actions of the individuals which influence him. The unknown function \phi is assumed to be decreasing fast. The aim of this paper is to estimate the unknown parameter p, in the asymptotic N to infinity, K to infinity and t to infinity. We denote by m{t} the average number of actions per individual until time t. We distinguish the subcritical case where m{t} increases linearly and the supercritical case where m{t} increases exponentially. We build some estimator of p in both cases.