# Accurate ranking of influential spreaders in networks based on dynamically asymmetric link-impact

## TL;DR

This paper introduces a novel asymmetric link-impact measure and s-shell decomposition for accurately ranking influential spreaders in networks, outperforming traditional degree and k-shell methods.

## Contribution

The paper presents a new asymmetric edge-weighting scheme and a weighted coreness measure that improve the identification of influential spreaders in complex networks.

## Key findings

- The proposed measures outperform degree and k-shell rankings in real-world networks.
- The methods maintain low computational complexity.
- Effective in applications like disease and information spread control.

## Abstract

We propose an efficient and accurate measure for ranking spreaders and identifying the influential ones in spreading processes in networks. While the edges determine the connections among the nodes, their specific role in spreading should be considered explicitly. An edge connecting nodes i and j may differ in its importance for spreading from i to j and from j to i. The key issue is whether node j, after infected by i through the edge, would reach out to other nodes that i itself could not reach directly. It becomes necessary to invoke two unequal weights wij and wji characterizing the importance of an edge according to the neighborhoods of nodes i and j. The total asymmetric directional weights originating from a node leads to a novel measure si which quantifies the impact of the node in spreading processes. A s-shell decomposition scheme further assigns a s-shell index or weighted coreness to the nodes. The effectiveness and accuracy of rankings based on si and the weighted coreness are demonstrated by applying them to nine real-world networks. Results show that they generally outperform rankings based on the nodes' degree and k-shell index, while maintaining a low computational complexity. Our work represents a crucial step towards understanding and controlling the spread of diseases, rumors, information, trends, and innovations in networks.