A credible property of resistance distance on real-world networks

On the basis of introducing the development of resistance distance, an important property of resistance distance was discussed. That is, Vertices in the same cluster of a graph have a small commute distance, whereas two vertices in different clusters of a graph have a “large” commute distance. The credible property was proved to be flawed on random geometric graphs by a research team. For the corrections of resistance distance mentioned by the research team, some experiments were made on real-world network data sets instead. The experiments showed that the property did not hold on rather small real-world network. Moreover, the computation results showed that the correction by von Luxburg did better than the correction by Brand.