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Fig. 3.12 Two networks with
similar number of nodes, but
different betweenness
Fig. 3.13 Two similar
networks with highlighted
bridges
highest betweenness and the outlying nodes have the minimum betweenness. The
structure of second network is cyclic; therefore, the value of betweenness is the
same for all nodes.
3.1.6.4 Bridge
The edge connecting the separate parts of network is called the bridge . Technically
speaking, removing this node from the network will increase the number of con-
nected components in the network. Finding bridges in the network can be very helpful
in the identification of important relations between nodes and also for finding
independent groups. An example of two contradictory networks with highlighted
bridges can be seen in Fig. 3.13 . The first one contains three bridges; the second one
is bridgeless.
3.1.6.5 Closeness Centrality
Closeness can be understood as a measure of how long it will take to distribute
some information from the given node to other reachable nodes in the network.
Closeness can be computed as
1
P t2Vv d
C C ð
v
Þ¼
Þ ;
ð
v
;
t
where d ( v , t ) is the shortest path between the nodes v and t in the given network.
Figure 3.14 illustrates two networks - the first one has dominant node in the center
of the network with the highest closeness value, and the second one has all nodes
with similar closeness value.
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