MATLAB: How to prevent the function rmnode from refreshing the nodes’ labels

Graph and Network Algorithmsgraph theoryundirected graph

I have a graph G which consists of 20 nodes, and I'm selecting a random node and remove it from the graph using rmnode. At each time my code check if all other nodes (one node at a time) after removing that node satisfies these two conditions:
  1. The specific node should not belong to the largest component
  2. The specific node does not have neighbors.
if one node satisfies these two conditions it should be removed.
How can I let rmnode not to refreshes the nodes' labels each time? 
G= WattsStrogatz(20,2,0.2);
% so=[1 1 1 2 2 2 2 3 3 3 5];
% ta=[2 3 4 3 4 5 6 6 7 5 7];
% G=graph(so,ta);
G=minspantree(G);
Hf=Cascading_Failure(G,1);
function Hf=Cascading_Failure(G,rmv)
N=numnodes(G);
subplot(2,2,1);
p=plot(G);
x=p.XData;
y=p.YData;
   
  
                    
attack=randsample(N,rmv);
Gf= rmnode(G,attack);
    x(attack)=[];
    y(attack)=[];
subplot(2,2,2);
plot(Gf,'XData',x,'YData',y)
[bin,binsize]=conncomp(Gf);
comp=length(binsize);
m=mode(bin);
o=find(bin==m); % members of largest component
    for i=1:length(attack)
        distance=distances(G,attack(i)); % distance vector ( Check the nodes based on their distance to node 'attack' )
        [~, idx]=sort(distance,'ascend');
       
        for j=2:length(distance)
            if ~ismember(idx(j),o) && isempty(neighbors(Gf,idx(j)))
                Gf=rmnode(Gf,idx(j));
                x(idx(j))=[];
                y(idx(j))=[];
                figure; plot(Gf,'XData',x,'YData',y)
            end
        end
    end
Hf=Gf;
end

Best Answer

If you use graph() or digraph() objects, then Nodes is a table, and you can add additional properties to the table including persistent labeling.
Consider too that instead of removing a node, that it can sometimes be as effective to remove all edges leading to it and from it, which has the advantage that the node numbers do not change.
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