Source-linked AI summary
Control centrality and hierarchical structure in complex networks
Yang-Yu Liu, Jean-Jacques Slotine, Albert-László Barabási
TL;DR
The paper addresses the unresolved role of each individual node in maintaining a network’s controllability by introducing control centrality for nodes in directed weighted networks. It relates control centrality to degree distribution and hierarchical position, while noting practical constraints on applying the resulting equation directly to real networks.
Problem
The role of each individual node in maintaining a system’s controllability remains an unanswered question.
Method
The paper defines control centrality for nodes using a weighted network wiring matrix and analyzes accessibility through directed stems.
Results
The distribution of control centrality is mainly determined by the underlying network’s degree distribution, and a hub reaching all nodes should have high control centrality.
Takeaways & Limitations
Control centrality connects node-level controllability with structural properties of the network.
Takeaways & Limitations
Applying the equation directly to real networks is constrained by the need for detailed knowledge of the control configuration and wiring diagram.
Abstract
from arXiv · showhide
We introduce the concept of control centrality to quantify the ability of a single node to control a directed weighted network. We calculate the distribution of control centrality for several real networks and find that it is mainly determined by the network's degree distribution. We rigorously prove that in a directed network without loops the control centrality of a node is uniquely determined by its layer index or topological position in the underlying hierarchical structure of the network. Inspired by the deep relation between control centrality and hierarchical structure in a general directed network, we design an efficient attack strategy against the controllability of malicious networks.