Fast asynchronous updating algorithms for k-shell indices

TL;DR

This paper introduces two fast asynchronous algorithms for calculating k-shell indices in large, dynamic networks, significantly reducing convergence time compared to previous methods.

Contribution

The paper presents two novel algorithms that improve the speed of k-shell index computation in large-scale, evolving networks, building on prior asynchronous methods.

Findings

Reduced convergence time up to 75.4% and 92.9% on real and artificial networks.

Algorithms effectively accelerate k-shell index calculations in large, dynamic networks.

Validated on multiple real-world and synthetic network datasets.

Abstract

Identifying influential nodes in networks is a significant and challenging task. Among many centrality indices, the $k$-shell index performs very well in finding out influential spreaders. However, the traditional method for calculating the $k$-shell indices of nodes needs the global topological information, which limits its applications in large-scale dynamically growing networks. Recently, L\@\"{u} \emph{et al.} [Nature Communications 7 (2016) 10168] proposed a novel asynchronous algorithm to calculate the $k$-shell indices, which is suitable to deal with large-scale growing networks. In this paper, we propose two algorithms to select nodes and update their intermediate values towards the $k$-shell indices, which can help in accelerating the convergence of the calculation of $k$-shell indices. The former algorithm takes into account the degrees of nodes while the latter algorithm prefers to choose the node whose neighbors' values have been changed recently. We test these two methods on four real networks and three artificial networks. The results suggest that the two algorithms can respectively reduce the convergence time up to 75.4\% and 92.9\% in average, compared with the original asynchronous updating algorithm.