Triangle randomization for social network data anonymization - Brankovic, Ljiljana (Ars mathematica contemporanea, 2014)
Let ?$G = (V, E)$? be a connected graph on n vertices. Denote by ?$\overline{l}(G)$? the average distance between all pairs of vertices in ?$G$?. The remoteness ?$ρ(G)$? of a connected graph? $G$? is the maximum average distance from a vertex of ?$G$? to all others. The aim of this paper is to show that two conjectures in M. Aouchiche and P. Hansen, Proximity and remoteness in graphs: results and conjectures, Networks 58 (2011), 95-102. concerned with average distance, radius and remoteness of a graph are true.
Keywords: distance; eccentricity; proximity; radius; remoteness