G = ( V, E) | a social network G with |V| nodes and |E| edges |
V | node set of G |
E | edge set of G |
| 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 |
| 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, ) | the distance of the shortest path between v and 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)}) |