G = ( V, E) a social network G with |V| nodes and |E| edges V node set of G E edge set of G $G\prime$ a generalized version of G G i  = (V i , E i ) a sub-graph of G where V = ∪i=1 to kV i and E i  ⊂ E ${v}_{i}^{c}$ the center of a sub-graph G i which is an insensitive node too v p node p Num(G i ) The number of nodes in G i Num(G i ,G j ) the number of nodes in G i that are adjacent to another subgraph G j SP D (v p ,v q ,G i ) the distance of the shortest path between nodes v p and v q in G i SPD(v, ${v}_{i}{C}^{}$) the distance of the shortest path between v and ${v}_{i}{C}^{}$ in G i Prob(SP D ( . )=β) The probability of the distance that equals to β S_SP D (G i ) shortest length of the shortest paths between any two nodes in G i (S_SPD(G i ) = { SPD(v m ,v n ,G i )| ∀ vp,v q ∈V i , SPD(v m ,v n ,G i ) ≤  SPD(v p ,v q ,G i )}) L_SP D (G i ) longest length of the shortest paths between any two nodes in G i (L_SPD(G i ) = { SPD(v m ,v n ,G i )| ∀ v p , v q ∈V i , SPD(v m ,v n ,G i ) ≥ SPD(v p ,v q ,G i )}) S_SPD(viC,Gi) shortest length of the shortest paths between viC and other nodes in G i (S_SPD(viC,Gi) = {SPD(vm,viC,Gi)| vp ϵV i , SPD(vm,viC,Gi) ≤ SPD(vp,viC,Gi)}) L_SPD(viC,Gi) longest length of the shortest paths between viC and other nodes in G i (L_SPD(viC,Gi) = {SPD(vm,viC,Gi)| vp ϵV i , SPD(vm,viC,Gi) ≥ SPD(vp,viC,Gi)})