what-when-how
In Depth Tutorials and Information
AdamicandAdar:
hese can be used to decide whether or not two Web pages
are strongly related. hrough this method they can calculate the similarity between
two pages as: ∑z:
1/
log(frequency(
z
)). he score(x,y) is calculated as: ∑z
∈
φ
(x)
∩
φ
(y)1/
log|
φ
(z) |.
Preferentialattachment
: his theory is based on an assumption that the future
edge that involves node x must belong to the set
φ
(x). So the probability of the col-
laboration between node x and y can be measured as: score(x,y) = |
φ
(x)|
.
|
φ
(y)|.
12.4.4 Mathematics of Centralities
In the social network, a node that directly connects with many nodes can be con-
sidered as a high degree node. In other words, the lower degree nodes need the high
degree nodes to serve as a bridge in order to connect with other lower degree nodes.
he high degree nodes can also be regarded as the information sources. Generally,
the degree or centrality Dc(aj) can be measured by:
=
Σ
1
Dc aj
(
)
n
d ai aj
(
,
)
i
⎩
1
ai and aj di
rectly connected
ai and aj not connected
d ai aj
(
,
)
=
where
0
his equation is useful for the subgraph of the whole network or a limited-size net-
work for centrality calculation. However, in most cases, we need to measure the rela-
tive centrality for different high degree nodes which are independent of each other.
For example, a maximum number of connected nodes for a certain graph is n
−
1. So
we need to introduce a new formula to calculate the centrality of the node by using
the proportion of the number of adjacent nodes to the maximum number (n
−
1).
Σ
1
i
n
d ai aj
n
(
,
)
=
D c aj
' (
)
−
1
Betweenness is one method to measure the centrality of a node in the network. If a
node is located in the middle of many shortest paths (geodesics) as an intermediate
between other nodes, this node has a higher betweenness than others. Typically,
in a network, G = <A,E>, where A denotes the nodes, and E denotes all the edges
between the nodes. he betweenness Bc(m) for a node m can be measured by:
aij m
aij
(
)
∑
Bc m
(
)
=
i
≠ ≠ ≠
j m v
where aij denotes the number of all the shortest paths between node i and j, and aij(m)
represents the number of all the shortest paths from i to j coming through the node m.
