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Spatial preferential attachment networks

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SNAW01 - Graph limits and statistics

We study a family of growing networks, in which new vertices are given a spatial position on the unit circle and are connected to existing vertices with a probability favouring short spatial distances and high degrees. In this model of a scale-free network with clustering we can independently tune the power law exponent τ of the degree distribution and the exponent δ at which the connection probability decreases with the distance of two vertices. We show that the network is robust if τ < 2 1/δ, but fails to be robust if τ > 2 1/(δ−1). This is the first instance of a scale-free network where robustness depends not only on its degree distribution but also on its clustering features. 

Joint work with Emmanuel Jacob (ENS Lyon).

This talk is part of the Isaac Newton Institute Seminar Series series.

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