2011/12/04 by Víctor M. Preciado, Preciado, Victor M., Michael M. Zavlanos +3 · 1 citation
Computer Science · Physics and Astronomy · #Complex Network Analysis Techniques #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Multiagent Systems (cs.MA) #Neural Networks Stability and Synchronization #Opinion Dynamics and Social Influence #Optimization and Control (math.OC) #Physics and Society (physics.soc-ph) #Social and Information Networks (cs.SI)
paper · pdf · doi:10.48550/arxiv.1112.0765
openalex publication_date 2011/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by the relationship between the eigenvalue spectrum of the Laplacian matrix of a network and the behavior of dynamical processes evolving in it, we propose a distributed iterative algorithm in which a group of n autonomous agents self-organize the structure of their communication network in order to control the network's eigenvalue spectrum. In our algorithm, we assume that each agent has access only to a local (myopic) view of the network around it. In each iteration, agents in the network peform a decentralized decision process to determine the edge addition/deletion that minimizes a distance function defined in the space of eigenvalue spectra. This spectral distance presents interesting theoretical properties that allow an efficient distributed implementation of the decision process. Our iterative algorithm is stable by construction, i.e., locally optimizes the network's eigenvalue spectrum, and is shown to perform extremely well in practice. We illustrate our results with nontrivial simulations in which we design networks matching the spectral properties of complex networks, such as small-world and power-law networks.