Wiener index versus Szeged index in networks

@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. 

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