Abstract
The principal eigenvalue of a network’s adjacency matrix often determines dynamics on the network (e.g., in synchronization and spreading processes) and some of its structural properties (e.g., robustness against failure or attack) and is therefore a good indicator for how “strongly” a network is connected. We study how is modified by the addition of a module, or community, which has broad applications, ranging from those involving a single modification (e.g., introduction of a drug into a biological process) to those involving repeated additions (e.g., power-grid and transit development). We describe how to optimally connect the module to the network to either maximize or minimize the shift in , noting several applications of directing dynamics on networks.
- Received 23 February 2011
DOI:https://doi.org/10.1103/PhysRevE.83.066112
©2011 American Physical Society