Extremal Properties of Complex Networks
Molecular Networks
2011-05-02 v1 Statistical Mechanics
Social and Information Networks
Physics and Society
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.
Cite
@article{arxiv.1104.5532,
title = {Extremal Properties of Complex Networks},
author = {Dionysios Barmpoutis and Richard M. Murray},
journal= {arXiv preprint arXiv:1104.5532},
year = {2011}
}