Extremal Properties of Complex Networks
arXiv:1104.5532
Abstract
We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph qualities for any arbitrary number of nodes and edges and analytically derive the form and properties of such networks.
References in corpus (5)
- Efficient Behavior of Small-World Networks
- Breakdown of the Internet under intentional attack
- Universal Behavior of Load Distribution in Scale-free Networks
- Networks with the Smallest Average Distance and the Largest Average Clustering
- Quantification and Minimization of Crosstalk Sensitivity in Networks