Compressive closeness in networks

Hamidreza Mahyar,Rouzbeh Hasheminezhad,H Eugene Stanley

doi:10.1007/s41109-019-0213-5

Abstract

Distributed algorithms for network science applications are of great importance due to today’s large real-world networks. In such algorithms, a node is allowed only to have local interactions with its immediate neighbors; because the whole network topological structure is often unknown to each node. Recently, distributed detection of central nodes, concerning different notions of importance, within a network has received much attention. Closeness centrality is a prominent measure to evaluate the importance (influence) of nodes, based on their accessibility, in a given network. In this paper, first, we introduce a local (ego-centric) metric that correlates well with the global closeness centrality; however, it has very low computational complexity. Second, we propose a compressive sensing (CS)-based framework to accurately recover high closeness centrality nodes in the network utilizing the proposed local metric. Both ego-centric metric computation and its aggregation via CS are efficient and distributed, using only local interactions between neighboring nodes. Finally, we evaluate the performance of the proposed method through extensive experiments on various synthetic and real-world networks. The results show that the proposed local metric correlates with the global closeness centrality, better than the current local metrics. Moreover, the results demonstrate that the proposed CS-based method outperforms state-of-the-art methods with notable improvement.

Highlights

Many real-world systems can be modeled by a network G = (V, E) of interacting actors
In “Experimental Evaluation” section, we experimentally show that the suggested local metric is highly correlated with the global closeness centrality on many real-world and synthetic networks
Evaluation Results Correlation between Our ego-Closeness and the Global Closeness We experimentally analyzed the correlation between the proposed ego-centric centrality metric and the global closeness centrality over several synthetic and real-world networks

Summary

Introduction

Many real-world systems can be modeled by a network G = (V , E) of interacting actors. The actors are demonstrated by a set of nodes V with cardinality |V | that are connected via the set of edges (links) E with cardinality |E|. Some well-known examples of such real-world systems include technological and transportation infrastructures, communication systems, biological networks, and social interactions. Centrality measures are means of quantifying the importance of a node within the given network. Proper quantification of importance should be done given the application context. To address applications in which reachability of a node to the entire network is of importance, researchers have introduced the closeness centrality measure. For an arbitrary node u, its closeness centrality C(u) is defined as the inverse of its average distance to the other nodes in the network.

Objectives

Methods

Results