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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)})