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Table 2 Notations and definitions

From: Social network integration and analysis using a generalization and probabilistic approach for privacy preservation

G = ( V, E) a social network G with |V| nodes and |E| edges
V node set of G
E edge set of G
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
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)})