what-when-how
In Depth Tutorials and Information
of the message transmission is equal to 1. After t iterations, the set At denotes all
the neighbors that can be reached from the origin node V0 at the time t. d(Vt,V0)
represents the number of t iterations.
At = {Vt: Vt
∈
V, d(Vt,V0) ≤ t}
η
i denotes the set of Vi's neighbors, Vi
∈
At.
η
i = {x, d(x,Vi) = 1} . hen At can be
given as:
∩
k
At = At
−
1U
(
−
1
η
i
)
For two selected nodes Vi and Vj, the possibility of being affected by the message
or information can be decided by the subset of all the paths among the two nodes.
For the given nodes Vi ,
α
1t represents all the nodes which are in the At, at a given
time t. In the simplest case, we assume V2 is the neighbor node of V1. At the time
t, the probability for the node V2 can be affected, which can be calculated as:
P1t = max (
α
1t, a1t, a2t)
Consider a two-path case where the message can be delivered from V1 origin to
V3. Assume nodes V2 and V4 are the intermediate carrier nodes. he formulation
can be given as:
P2t = max(
α
2t,a3t,a2t, a1t, a3t, a4t, a1t)
In the general case, for
n
paths from any given nodes to others, the possibility
κ
(A,B) denotes all the paths between the nodes A and B:
∏
∏
∏
= ∏
Pnt =max ant
{
,
n
kit
n
k t
2
, .......
.,
n
(
k n
1
),
n
knt
}
i
=1
i
=1
i
=1
i
=1
12.7 Conclusions
his chapter discussed some popular issues in social network protocol designs, such
as security, link prediction issue, terrorist network issue, and disconnected cluster
communication issue. here are still many challenging problems to be solved in
order to build a robust social network.
References
1. Banks, L., Ye, S., Huang, Y., and Wu, S. F. 2007. Davis social links: integrating social
networks with internet routing. In
Proceedings of the 2007Workshop on Large Scale
AttackDefense
(Kyoto, Japan, August 27-27, 2007). LSAD' 07. ACM, New York, NY,
121-128.
