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binary_search_filter_1 <- function(g, low, high) {
  x<-g
  if ( high < low ) {
    
    return(NULL)
    
  }else {
    mid <- floor((low + high) / 2)
    x<-igraph::delete.edges(g, which(E(g)$weight <= weights[mid])) 
    cat("low:", low, " mid:", mid, " high:", high, " mid_weight:", weights[mid], " components:", count_components(x), " edges:", ecount(x), "\n")
    
    if ((mid - low) == 0){
      x<-igraph::delete.edges(g, which(E(g)$weight <= weights[mid-1])) 
      cat("Final: low:", low - 1, " mid:", mid - 1, " high:", high - 1, " mid_weight:", weights[mid - 1], " components:",count_components(x), " edges:", ecount(x), "\n")
      return(list(weight=mid - 1, graph=x))
      exit
    }
    
    if (((high - low) == 0)){
      x<-igraph::delete.edges(g, which(E(g)$weight <= weights[mid+1])) 
      cat("Final: low:", low, " mid:", mid, " high:", high, " mid_weight:", weights[mid], " components:",count_components(x), " edges:", ecount(x), "\n")
      return(list(weight=mid , graph=x))
      exit
    }
    
    
    if (!(is.connected(x))){
      binary_search_filter_1(g, low, mid - 1)
    }else if (is.connected(x)){
      binary_search_filter_1(g, mid + 1, high)
    }
  }
}

weights <- unique(sort(E(G)$weight, decreasing = FALSE))
binary_search_filter_1(g = G, low = 1, high = length(weights))$graph