Algorithm A1 Calculate correlations

Require: multiple initial set of opinions ${\{\mathbf{S}}_i{\}}_{initial}$ and the adjacency matrix of the embedding network $A_{ij}$. Number of repetitions $N_{reps}$ Ensure: a correlation matrix $C_{ij}$ that contains the number of times a pair of nodes has the same final opinion in the steady state when running a Metropolis algorithm $N_{reps}$ times

set ${\widehat{C}}_{ij}=0\forall i,i$  set $rep=0$  repeat   set initial opinion ${\left\{{\mathbf{S}}_{\mathbf{i}}\right\}}_{\mathbf{initial}}$ uniformly at random   call a Metropolis algorithm   define correlation value for each pair of nodes   for all ${\mathbf{S}}_{\mathbf{i}},{\mathbf{S}}_{\mathbf{j}}\in {\left\{{\mathbf{S}}_{\mathbf{i}}\right\}}_{\mathbf{final}}$ with i, j $\in 1,...,N$ do     if ${\mathbf{S}}_{\mathbf{i}}={\mathbf{S}}_{\mathbf{j}}$ then       ${\widehat{C}}_{ij}\leftarrow {\widehat{C}}_{ij}+1$     else       ${\widehat{C}}_{ij}\leftarrow {\widehat{C}}_{ij}-1$     end if   end for   $rep\leftarrow rep+1$ until$rep=N_{reps}$ return${\widehat{C}}_{ij}/N_{reps}$ as $C_{ij}$ correlation matrix