Let G = (V,E) is a graph, we have to pick K vital nodes in the network that are capable to spread the information throughout the network. So, how we can define? Either we are going to pick set of key players or K individual players.
Research paper is attached here and link is also given.
The action of each player in network affects the others actions. So if you are plan to find k-key players, its much better if you choose a method that takes this influence into account (I mean you better not to simply calculate a centrality measure and choose k individuals with highest scores based on this measure since most of the centrality measures considers the nodes isolated).
You can use some centralities which are defined on group of nodes, or run any dynamical processes such as "random walk" or any epidemic spreading models initially starting from k nodes (run multiple random walk concurrently, each one starting from one of the k nodes) and calculate the percentage of infected nodes after n steps to find the importance of k selected nodes.
Also consider that the selection of a proper method is directly depends on your application.
If you are interested in taking K vital nodes then each node should have high importance. So better to select the most important player (s) depending upon some measure like Katz centrality and go down till you get K of them.
B.K. Tripathy
is there any difference between K vital nodes and set of k-vital nodes?
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