Power of individuals -- Controlling centrality of temporal networks

TL;DR

This paper introduces graphic tools to analyze the structural controllability of temporal networks, revealing the intrinsic control mechanisms of individuals and the robustness of controlling centrality across various network types.

Contribution

It develops analytical bounds for controlling centrality in temporal networks and classifies temporal trees to understand control dynamics, a novel approach in this field.

Findings

Controlling centrality follows a scale-free distribution.

The distribution is independent of time scale and dataset type.

Numerical simulations verify the theoretical bounds.

Abstract

Temporal networks are such networks where nodes and interactions may appear and disappear at various time scales. With the evidence of ubiquity of temporal networks in our economy, nature and society, it's urgent and significant to focus on structural controllability of temporal networks, which nowadays is still an untouched topic. We develop graphic tools to study the structural controllability of temporal networks, identifying the intrinsic mechanism of the ability of individuals in controlling a dynamic and large-scale temporal network. Classifying temporal trees of a temporal network into different types, we give (both upper and lower) analytical bounds of the controlling centrality, which are verified by numerical simulations of both artificial and empirical temporal networks. We find that the scale-free distribution of node's controlling centrality is virtually independent of the time scale and types of datasets, meaning the inherent heterogeneity and robustness of the controlling centrality of temporal networks.