Define similarity when a network is concerned. Why is the similarity score important in a real-world network? What can be inferred if the similarity scores of two network nodes are comparable? Can similarity alone transform a random network to a scale-free network? Dis- cuss.

Question

What will be an ideal response?

Answer 1

In a network, similarity can be identified by similar ranked nodes where the nodal ranking
is carried out on the basis of degree. In real-world networks, similarity can be identified by
profession, financial status, social status, interest, etc. For example, a comic book seller and a
super hero toy seller are mostly targeting similar age group of kids and they can be considered
as similar in terms of targeted customers. Further, there also have certain similarity between
a general book seller and the comic book seller as well as the super hero toy seller and a
barbie doll seller.
The similarity score is important to identify the cluster of similar nodes and their relationships.
Therefore, with comparable similarity score, one can identify that the nodes share similar
interest/traits as mentioned above.
However, similarity identifies only a set of communities (with similar interest) in a network.

In order to transform the network to a scale-free network, we need to optimize the prod-
uct of the similarity and node popularity scores.