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G = ( V, E)
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a social network G with |V| nodes and |E| edges
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V
|
node set of G
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E
|
edge set of G
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|
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a generalized version of G
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G
i
= (V
i
, E
i
)
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a sub-graph of G where V = ∪i=1 to kV
i
and E
i
⊂ E
|
|
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the center of a sub-graph G
i
which is an insensitive node too
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v
p
|
node p
|
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Num(G
i
)
|
The number of nodes in G
i
|
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Num(G
i
,G
j
)
|
the number of nodes in G
i
that are adjacent to another subgraph G
j
|
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SP
D
(v
p
,v
q
,G
i
)
|
the distance of the shortest path between nodes v
p
and v
q
in G
i
|
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SPD(v, )
|
the distance of the shortest path between v and in G
i
|
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Prob(SP
D
(
.
)=β)
|
The probability of the distance that equals to β
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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)})
|
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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)})
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