Algorithm A1 Program Flow: Growth of the graph by attaching simplexes with defects

1:INPUT:$n_{min}$, $n_{max}$, $N_{max}$, p 2:initialise graph $\mathcal{G}$ as a simplex of size n taken from the distribution $p_n=A{n}^{-2}$, which is defined in the range $[n_{min},n_{max}]$ 3:initialise set of defected edges $\mathcal{D}$ as an empty set 4: while $N<N_{max}$ do 5:   select new simplex size $n_{new}\in [n_{min},n_{max}]$ from the distribution $p_n$ 6:   randomly select the docking site as a simplex $\sigma \in \mathcal{G}$ with folowing constraints: (1) order $q_{\sigma }<n_{new}-1$; (2) $\sigma$ is not in set of defected edges $\mathcal{D}$; and (3) $\sigma$ does not contain any edge from $\mathcal{D}$ 7:   form a new simplex ${\sigma }_{new}$ by attaching $n_{new}-q_{\sigma }-1$ new nodes to the $q_{\sigma }+1$ nodes of the docking simplex $\sigma$ 8:   if random number <p then 9:     if $\sigma$ contains at least one of defected nodes (ends of defected edge) then 10:       Chose randomly a defected node a from $\sigma$ and randomly b as one of $n_{new}-q_{\sigma }-1$ new nodes 11:       Add edge $(a,b)$ to $\mathcal{D}$ 12:     else 13:       Chose randomly one of newly added edges $(a,b)$ and add to $\mathcal{D}$ 14:     end if 15:   end if 16:   sampling the data of interest; 17:end while  18:END