Abstract:
Closeness centrality is one way of measuring how
central a node is in the given network. The closeness centrality
measure assigns a centrality value to each node based on its
accessibility to the whole network. In real life applications, we
are mainly interested in ranking nodes based on their centrality
values. The classical method to compute the rank of a node
first computes the closeness centrality of all nodes and then
compares them to get its rank. Its time complexity is O(n·m+n),
where n represents total number of nodes, and m represents
total number of edges in the network. In the present work, we
propose a heuristic method to fast estimate the closeness rank
of a node in O(α · m) time complexity, where α = 3. We also
propose an extended improved method using uniform sampling
technique. This method better estimates the rank and it has the
time complexity O(α·m), where α ≈ 10−100. This is an excellent
improvement over the classical centrality ranking method. The
efficiency of the proposed methods is verified on real world scalefree social networks using absolute and weighted error functions.
