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a
b
M
(
S
) =1.429
M
(
S exp )=2.4
Fig. 5.4 An example of maximizing the local modularity of the expanding community. In
Fig. 5.4a the local modularity of the subgraph consisting of nodes 1-6 has a value of
M
429. By attaching node 11 to the community (Fig. 5.4b ), the local modularity of the
expanded subgraph (comprising nodes 1-6 and 11) is now equal to M
¼
10
7 ¼
1
:
12
5
ð
S exp Þ¼
¼
2
:
4
After carrying out the community expansion step, there are still nodes that have
no community associated with them. These nodes are classified as either hubs or
outliers using the same criterion as in [ 4 ]. A node is considered to be a hub if it is
connected to more than one community. For instance, node 8 in Fig. 5.2 is classified
as a hub since it is adjacent to two communities. The remaining nodes, i.e., nodes
that are adjacent to only one or no community at all are classified as outliers.
In Fig. 5.2 , node 7 is such a node. In the case of tag networks, hub tags may
correspond to either polysemous tags that are used in multiple topical contexts or
generic tags that can be used independent of the topic of a resource (for instance, in
 
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