Social Network Analysis in Community-Built Databases - Community-Built Databases: Research and Development - page 60

Fig. 3.10 Two similar
networks with different
degrees (average degrees 1.6
and 2)

Fig. 3.11 Two similar networks with different degrees (average degrees 2.5 and 3.3) and their
histograms

3.1.6.2 Degree Centrality

To evaluate the degree of the node with respect to the whole network, we can also
use so-called degree centrality , which can be computed as

degree ð v Þ

C D ð v Þ¼ ;

n 1

where n is the number of the nodes in the network. This measure can be extended to
the whole network using the node with highest degree centrality as a baseline.

3.1.6.3 Betweenness

Relative importance of the node in the network - with respect to the transmission of
information through the network - can be represented using betweenness . For a
graph (or network) G ¼ ( V , E ), this measure can be computed using

X

s st ð

v Þ

C B ð v Þ¼ ;

s st

s6¼v6¼t2V

where

s st ( v ) is the
number of shortest paths between the nodes s and t that pass through the node v .
Figure 3.12 contains two networks with a similar number of nodes, but different
inner structure, which results in a different betweenness value of nodes. The
first network has a hierarchical structure; therefore, the central node has the

s st is the number of shortest paths between the nodes s and t ,