Describe the procedure that you will adopt to identify a popular node. Is popularity a key property for transforming a random network to scale-free? Provide reasons for your answer.

What will be an ideal response?

One way of identifying popular nodes in a network is by estimating degree of all nodes and
then ranking them according to the degree-values. The highest ranked node in the network
can be treated as the most popular node in the network. Note that the connections can be
of two types: undirected and directed. In case of undirected connections, the total number
of connections can be considered as degree of the node. On the other hand, for directed
networks, in-degree and out-degree have to be measured separately.
Popularity plays a major role in the transformation of a network to a scale-free network.
Popularity can be judged by the origination time of a certain node in the network. Therefore,
older nodes have higher chance of being popular. In another sense, the phenomenon of
preferential attachment can be realized by identifying popular nodes with respect to higher
degree-based ranking. However, only popularity may not always result in scale-free network
creation.