UTRC CDS Lecture: Victor Preciado, "From Local Network Structure to Global Graph Spectrum"
Friday, January 23, 2015
1146 A V Williams
301 405 6576
United Technologies Research Center
Invited Lectures on Control and Dynamical Systems
From Local Network Structure to Global Graph Spectrum
Raj and Neera Singh Assistant Professor of Electrical and Systems Engineering
Networked & Social Systems Engineering program
Warren Center for Network & Data Sciences
University of Pennsylvania
Using methods from algebraic graph theory and convex optimization we study the relationship between local structural features of a network and global spectral properties. In particular, we derive expressions for the so-called spectral moments of a graph in terms of local structural measurements, such as subgraph densities. Furthermore, we propose a series of semidefinite programs to compute bounds on the spectral radius, and other spectral properties, from a truncated sequence of spectral moments. Using our tools, we illustrate how important spectral properties of real-world networks are strongly constrained by local structural features.
Victor M. Preciado is the Raj and Neera Singh Assistant Professor of Electrical and Systems Engineering at the University of Pennsylvania, where he is affiliated with the Networked & Social Systems Engineering program and the Warren Center for Network & Data Sciences. He received his Ph.D. degree in Electrical Engineering and Computer Science from MIT. He has also been a visiting scientist at UC Berkeley and Santa Fe Institute. His main research interests lie in the modeling, analysis, control, and optimization of large-scale complex dynamic networks, with applications in social networks, technological infrastructure, and biological systems.