An Estimation of the Shortest and Largest Average Path Length in Graphs of Given Density
Physics and Society
2015-03-17 v1 Social and Information Networks
Abstract
Many real world networks (graphs) are observed to be 'small worlds', i.e., the average path length among nodes is small. On the other hand, it is somewhat unclear what other average path length values networks can produce. In particular, it is not known what the maximum and the minimum average path length values are. In this paper we provide a lower estimation for the shortest average path length (l) values in connected networks, and the largest possible average path length values in networks with given size and density. To the latter end, we construct a special family of graphs and calculate their average path lengths. We also demonstrate the correctness of our estimation by simulations.
Cite
@article{arxiv.1101.2549,
title = {An Estimation of the Shortest and Largest Average Path Length in Graphs of Given Density},
author = {László Gulyás and Gábor Horváth and Tamás Cséri and George Kampis},
journal= {arXiv preprint arXiv:1101.2549},
year = {2015}
}