what-when-how
In Depth Tutorials and Information
Freeman has introduced another method to calculate the relative centrality of
any node in the network.
Bc m
(
)
B c m
'
(
)
=
−
+
(
n
2
3
n
2 2
)
/
his formula is tentative to calculate the relative betweenness of a node in the net-
work. In fact, this method is a way to normalize Bc(m) by dividing the maximum
number ((n-1)(n-2)) of nodes it connected to.
In Figure 12.2, node 1 can reach every node in the graph except node 5, so
it has the higher closeness than other nodes; in other words, we can say node 1 is
closer to all the nodes in the network.
he simplest way to measure the closeness centrality is to calculate the sum of
the geodesics distance from one node to all other nodes in the network and then
take its inverse. With the increase of the distance from node m to other nodes, the
closeness will increase as well. he formula can be given by:
Cc m
(
)
=
[
Σ
1
i
n
d m j
(
, )]
−
1
=
where d is the shortest path between nodes m and j. he relative closeness can be
measure by:
−
n
d m j
1
Cc m '
(
)
=
Σ
[
i
n
(
, )]
−
1
=
1
1
3
2
4
6
5
Figure 12.2
A graph example. (From Kossinets, G., Kleinberg, J., and Watts,
D. 2008.
Proceeding of the 14th ACM SIGKDD International Conference on
Knowledge Discovery and Data Mining
[LasVegas,Nevada,August24-27,2008].
KDD'08.ACM,NewYork,435-443.)
