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Spatial preferential attachment networks

Presented by: 
Peter Morters University of Bath
Friday 15th July 2016 - 09:00 to 09:30
INI Seminar Room 1
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).
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons