Distributed Identification of Central Nodes with Less Communication

Abstract

This paper is concerned with distributed detection of central nodes in complex networks using closeness centrality. Closeness centrality plays an essential role in network analysis. Distributed tasks such as leader election can make effective use of centrality information for highly central nodes, but complete network information is not locally available. Evaluating closeness centrality exactly requires complete knowledge of the network; for large networks, this may be inefficient, so closeness centrality should be approximated. Here, situations for decentralised network view construction where a node has zero knowledge about other nodes on the network at initial and there is no central node to coordinate evaluations of node closeness centrality are considered. Unlike centralized methods for detection of central nodes, in decentralized methods an approximated view of the network must be available at each node, then each node can evaluate its own closeness centrality before it can share it with others when applicable. Based on our knowledge, there is no much work done under this setting where the leading approach consists of running the breadth-first search Skiena (1998) on each node with a limited number of iterations (which is less than the diameter of the graph into consideration), as done by You et al. (2017), Wehmuth and Ziviani (2012), before each node evaluates its centrality. Running the breadth-first search on each node in a decentralized fashion requires high cost in terms of communication. Our contribution is to consider a better way of constructing network view in a decentralised manner with less communication cost. This paper refines a distributed centrality computation algorithm by You et al. (2017) by pruning nodes which are almost certainly not most central. For example, in a large network, leave nodes can not play a central role. This leads to a reduction in the number of messages exchanged to determine the centrality of the remaining nodes. Our results show that our approach reduces the number of messages for networks which contain many prunable nodes. Our results also show that reducing the number of messages may have a positive impact on running time and memory size.