@article{Klavzar2013WienerIV,
title={Wiener index versus Szeged index in networks},
author={Sandi Klavzar and Mohammad J. Nadjafi-Arani},
journal={Discrete Applied Mathematics},
year={2013},
volume={161},
pages={1150-1153}
}

Let (G, w) be a network, that is, a graph G = (V (G), E(G)) together with the weight function w : E(G) → R. The Szeged index Sz(G, w) of the network (G, w) is introduced and proved that Sz(G, w) ≥ W (G, w) holds for any connected network where W (G, w) is the Wiener index of (G, w). Moreover, equality holds if and only if (G, w) is a block network in which w is constant on each of its blocks. Analogous result holds for vertex-weighted graphs as well.