A heuristic approach to estimate nodes’ closeness rank using the properties of real world networks

Abstract

Centrality measures capture the intuitive notion of the importance of a node in a network. Importance of a node can be a very subjective term and is defined based on the context and the application. Closeness centrality is one of the most popular centrality measures which quantifies how close a node is to every other node in the network. It considers the average distance of a given node to all the other nodes in a network and requires one to know the complete information of the network. To compute the closeness rank of a node, we first need to compute the closeness value of all the nodes, and then compare them to get the rank of the node. In this work, we address the problem of estimating the closeness centrality rank of a node without computing the closeness centrality values of all the nodes in the network. We provide linear time heuristic algorithms which run in O(m), versus the classical algorithm which runs in time \(O(m \cdot n)\), where m is the number of edges and n is the number of nodes in the network. The proposed methods are applied to real-world networks, and their accuracy is measured using absolute and weighted error functions.