et $\mathcal Z=(z_{ij}(T))_{0\leq i,j\leq V}$ be the adjacency matrix defined by $z_{ij}(T)=0$ if there is at least one interaction between $i$ and $j$ in the interval $[0,T]$, and 0 otherwise. We have $$\begin{aligned} \pi(\phi,\xi|\mathcal D)&=\pi(\phi,\xi|\mathcal D,\mathcal Z)=\pi(\xi|\mathcal D,\mathcal Z)\pi(\phi|\xi ,\mathcal D).\end{aligned}$$ The idea of the two-step procedure is to 