  The Axelrod model has been widely studied since its proposal for social
influence and cultural dissemination. In particular, the community of
statistical physics focused on the presence of a phase transition as a function
of its two main parameters, $F$ and $Q$. In this work, we show that the Axelrod
model undergoes a second order phase transition in the limit of $F \rightarrow
\infty $ on a complete graph. This transition is equivalent to the
Erd\"os-R\'enyi phase transition in random networks when it is described in
terms of the probability of interaction at the initial state, which depends on
a scaling relation between $F$ and $Q$. We also found that this probability
plays a key role in sparse topologies by collapsing the transition curves for
different values of the parameter $F$.
