A k-shell decomposition method for weighted networks

TL;DR

This paper introduces a generalized weighted k-shell decomposition method that considers both weights and degrees, providing a more refined network partitioning and better identification of influential nodes, validated through simulations and real-world networks.

Contribution

The paper presents a novel weighted k-shell decomposition method that extends the classic approach to weighted networks, improving node ranking and core identification without arbitrary thresholds.

Findings

Weighted k-shell better ranks influential nodes in spreading processes

Method produces more meaningful cores in economic networks

Refines network partitioning by incorporating weights and degrees

Abstract

We present a generalized method for calculating the k-shell structure of weighted networks. The method takes into account both the weight and the degree of a network, in such a way that in the absence of weights we resume the shell structure obtained by the classic k-shell decomposition. In the presence of weights, we show that the method is able to partition the network in a more refined way, without the need of any arbitrary threshold on the weight values. Furthermore, by simulating spreading processes using the susceptible-infectious-recovered model in four different weighted real-world networks, we show that the weighted k-shell decomposition method ranks the nodes more accurately, by placing nodes with higher spreading potential into shells closer to the core. In addition, we demonstrate our new method on a real economic network and show that the core calculated using the weighted k-shell method is more meaningful from an economic perspective when compared with the unweighted one.