Optimal Control Approach to Network Centrality
Abstract
The objective of this proposal is to provide a control theoretic framework to node centrality in networks. Centrality is a recurrent theme in Network Science and the typical approach is to identify central nodes according to some heuristic notion and perform ranking of nodes based on it. In contrast, we argue that more useful notions arise if one ties centrality to network dynamics and relates it to the control objective that such dynamics wish to achieve. Thus, in this proposal we argue that a node cannot be central per se, but its centrality should be considered with respect to the given task we wish to achieve. This control-theoretic notion of centrality has broad applicability in many practical scenarios, where there are dynamical processes occurring over networks. Despite such applications, the classical approach to node centrality only accounts for network structure but fails to incorporate dynamical systems and control issues. We adopt the following framework- given a dynamical network of agents, determine what are the most suitable nodes to control in order to reach a certain objective. Within this framework, we consider both minimum-energy and minimum-time centrality measures and explore their properties for both linear and nonlinear system dynamics. We also consider how these centrality measures are impacted when one considers the presence of external inputs to the network and how concepts can be generalized to other variational notions of centrality. Finally, we consider the case when the dynamics over the network are time-varying. This is motivated by the fact that due to random encounters, link-failures, node-failures, etc., nearly all social, economic, and technological networks are time-varying. Our work formulates new centrality concepts that are applicable in all of these cases and are meaningful from both the dynamical system and the network science viewpoints.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 06, 2025
- Source ID
- FA95502410129
Entities
People
- Massimo Franceschetti
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of California, San Diego