Online Estimating The Top k Nodes Of A Network

The goal of this paper is to estimate the top k central nodes in a network through parsimonious sampling, in an online fashion. We consider three centrality metrics: degree, betweenness, and closeness centrality. We identify and investigate through simulations the contributions of two sources of error in finding central nodes: (1) sampling (collection) error and (2) identification error. Sampling error occurs when a node in the top k most central nodes is not sampled by the sampling algorithm. Identification error occurs when a sampled top k node is not identified as such. We observe that among the analyzed traces, random walks yield low sampling error. Using degree centrality as an alias for identifying nodes with high betweenness and closeness centrality, we then show that degree information collected while sampling the network can be used to reduce identification errors. As a consequence of these two observations, a random walk using degree to identify the top k betweenness and closeness central nodes performs better, in the analyzed traces, for small values of sampled fraction of nodes (1-5%), than more complex strategies recently proposed in the literature.