In Gephi I visualized a graph to calculate the eigenvalues,then I choose a portion of graph (e.g 6 vertex with their edges) and delete all others. I calculate the eigenvalues again and noticed that I get the same result.By same result I mean same ranking but with different values. The question is if this is happens by chance(I tried three times) or there is a mathematical fact back of it? If yes, what theorem should I search for? or if anybody can explain here and give a proof of it I'll be appreciate it.
Thanks alot, Behzad