diff --git a/R/output_utils.R b/R/output_utils.R
index 07007ead..f522fa63 100644
--- a/R/output_utils.R
+++ b/R/output_utils.R
@@ -99,20 +99,19 @@ prepare_output_bgm = function (
     colnames(results$inclusion_indicator_samples) = edge_names
   }
 
+  results$arguments = arguments
+  class(results) = "bgms"
+  
   # SBM postprocessing
   if (edge_selection && edge_prior == "Stochastic-Block" && "allocations" %in% names(out)) {
-    results$allocations <- out$allocations
+    results$arguments$allocations = out$allocations
     # Requires that summarySBM() is available in namespace
-    sbm_summary <- summarySBM(list(
-      indicator = results$inclusion_indicator,
-      allocations = results$allocations
-    ), internal_call = TRUE)
-    results$components <- sbm_summary$components
-    results$allocations <- sbm_summary$allocations
+    sbm_summary = summarySBM(results, internal_call = TRUE) 
+    results$components = sbm_summary$components
+    results$allocations = sbm_summary$allocations
   }
 
-  results$arguments = arguments
-  class(results) = "bgms"
+
   return(results)
 }
 
diff --git a/R/posterior_utils.R b/R/posterior_utils.R
index 71336b78..d51fc0fb 100644
--- a/R/posterior_utils.R
+++ b/R/posterior_utils.R
@@ -121,10 +121,9 @@ summarySBM = function(
   if(arguments$save == FALSE && internal_call == FALSE)
     stop('The bgm function must be run with save = TRUE.')
 
-  cluster_allocations = bgm_object$allocations
+  cluster_allocations = arguments$allocations
   dirichlet_alpha = arguments$dirichlet_alpha
   lambda = arguments$lambda
-
   # Pre-compute log_Vn for computing the cluster probabilities
   num_variables = ncol(cluster_allocations)
   log_Vn = compute_Vn_mfm_sbm(
diff --git a/src/gibbs_functions_edge_prior.cpp b/src/gibbs_functions_edge_prior.cpp
index 3650acfd..4155f7de 100644
--- a/src/gibbs_functions_edge_prior.cpp
+++ b/src/gibbs_functions_edge_prior.cpp
@@ -62,30 +62,16 @@ arma::vec compute_Vn_mfm_sbm(arma::uword no_variables,
   double r;
   double tmp;
 
-  for(arma::uword t = 1; t <= t_max; t++) {
+  for(arma::uword t = 0; t < t_max; t++) {
     r = -INFINITY;
-    for(arma::uword k = t; k < 500; k++) {
-      tmp = 0.0;
-      for(arma::uword tt = 1 - t; tt < 1; tt ++) {
-        tmp += std::log(dirichlet_alpha * k + tt);
-      }
-      for(arma::uword n = 0; n < no_variables; n++) {
-        tmp -= std::log(dirichlet_alpha * k + n);
-      }
-      tmp -= std::lgamma(k + 1);
-
-      // Add the poisson term
-      double log_norm_factor = log(1.0 - exp(R::dpois(0, lambda, true)));
-      tmp += R::dpois(k-1, lambda, true) - log_norm_factor;
-
-      // Compute the maximum between r and tmp
-      if (tmp > r) {
-        r = std::log(std::exp(r - tmp) + 1) + tmp;
-      } else {
-        r = std::log(1 + std::exp(tmp - r)) + r;
-      }
+    for(arma::uword k = t; k <= 500; k++){
+      arma::vec b_linspace_1 = arma::linspace(k-t+1,k+1,t+1);
+      arma::vec b_linspace_2 = arma::linspace((k+1)*dirichlet_alpha,(k+1)*dirichlet_alpha+no_variables-1, no_variables);
+      double b = arma::accu(arma::log(b_linspace_1))-arma::accu(arma::log(b_linspace_2)) + R::dpois((k+1)-1, lambda, true);
+      double m = std::max(b,r);
+      r = std::log(std::exp(r-m) +  std::exp(b-m)) + m;
     }
-    log_Vn(t-1) = r - std::log(std::exp(1) - 1);
+    log_Vn(t) = r;
   }
   return log_Vn;
 }
@@ -129,24 +115,20 @@ double log_marginal_mfm_sbm(arma::uvec cluster_assign,
                             double beta_bernoulli_alpha,
                             double beta_bernoulli_beta) {
 
-  arma::uword no_clusters_excl_node = arma::max(cluster_assign);
-  //*std::max_element(cluster_assign.begin(), cluster_assign.end());
+  arma::uvec indices = arma::regspace<arma::uvec>(0, no_variables-1);
+  arma::uvec select_variables = indices(arma::find(indices != node));          
+  arma::uvec cluster_assign_wo_node = cluster_assign(select_variables);
+  arma::uvec indicator_node = indicator.col(node); 
+  arma::vec gamma_node = arma::conv_to<arma::vec>::from(indicator_node(select_variables));
+  arma::uvec table_cluster = table_cpp(cluster_assign_wo_node);
   double output = 0;
-  double sumG;
-  double sumN;
-
-  output -= no_clusters_excl_node * R::lbeta(beta_bernoulli_alpha, beta_bernoulli_beta);
-
-  for(arma::uword c = 0; c < no_clusters_excl_node; c++) {
-    sumG = 0;
-    sumN = 0;
-    for(arma::uword i = 0; i < no_variables; i++) {
-      if(cluster_assign(i) == c) {
-        sumG += static_cast<double>(indicator(node, i));
-        sumN += 1.0;
-      }
+  for(arma::uword i = 0; i < table_cluster.n_elem; i++){
+    if(table_cluster(i) > 0){ // if the cluster is empty (it is the previous cluster of 'node' where 'node' was the only member - a singleton, thus skip)
+      arma::uvec which_variables_cluster_i = arma::find(cluster_assign_wo_node == i);
+      double sumG = arma::accu(gamma_node(which_variables_cluster_i));
+      double sumN = static_cast<double>(which_variables_cluster_i.n_elem);
+      output += R::lbeta(sumG + beta_bernoulli_alpha, sumN - sumG + beta_bernoulli_beta) - R::lbeta(beta_bernoulli_alpha, beta_bernoulli_beta);
     }
-    output += R::lbeta(sumG + beta_bernoulli_alpha, sumN - sumG + beta_bernoulli_beta);
   }
   return output;
 }