# Influencer identification in dynamical complex systems

## TL;DR

This review surveys recent methods for identifying key influencers in complex systems, focusing on structural importance and dynamic impact, with applications across various disciplines.

## Contribution

It provides a comprehensive overview of state-of-the-art influencer identification techniques from multiple perspectives and objectives.

## Key findings

- Discusses minimal node removal for network breakdown
- Surveys methods for locating nodes affecting global dynamics
- Highlights differences between structural and dynamic influencer identification

## Abstract

The integrity and functionality of many real-world complex systems hinge on a small set of pivotal nodes, or influencers. In different contexts, these influencers are defined as either structurally important nodes that maintain the connectivity of networks, or dynamically crucial units that can disproportionately impact certain dynamical processes. In practice, identification of the optimal set of influencers in a given system has profound implications in a variety of disciplines. In this review, we survey recent advances in the study of influencer identification developed from different perspectives, and present state-of-the-art solutions designed for different objectives. In particular, we first discuss the problem of finding the minimal number of nodes whose removal would breakdown the network (i.e., the optimal percolation or network dismantle problem), and then survey methods to locate the essential nodes that are capable of shaping global dynamics with either continuous (e.g., independent cascading models) or discontinuous phase transitions (e.g., threshold models). We conclude the review with a summary and an outlook.