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Rumour spreading is a protocol for modelling the spread of informationthrough a network via user-to-user interaction. The Spatial PreferredAttachment (SPA) model is a random graph model for complex networks: verticesare placed in a metric space, and the link probability depends on the metricdistance between vertices, and on their degree. We show that the SPA modeltypically produces graphs that have small effective diameter, i.e. $O(\log^2n)$, while rumour spreading is relatively slow, namely polynomial in $n$.

Rumours spread slowly in a small world spatial network