Graph centrality is a question of scale Alexis Arnaudon,1 Robert L. Peach,1, 2 and Mauricio Barahona1, ∗ 1 Department of Mathematics, Imperial College London, London SW7 2AZ, UK 2 Imperial College Business School, Imperial College London, London SW7 2AZ, UK...
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Graph centrality is a question of scale Alexis Arnaudon,1 Robert L. Peach,1, 2 and Mauricio Barahona1, ∗ 1 Department of Mathematics, Imperial College London, London SW7 2AZ, UK 2 Imperial College Business School, Imperial College London, London SW7 2AZ, UK Classic measures of graph centrality capture distinct aspects of node importance, from the local (e.g., degree) to the global (e.g., closeness). Here we exploit the connection between diffusion and geometry to introduce a multiscale centrality measure. A node is defined to be central if it breaks the metricity of the diffusion as a consequence of the effective boundaries and inhomogeneities in the graph. Our measure is naturally multiscale, as it is computed relative to graph neighbourhoods within the varying time horizon of the diffusion. We find that the centrality of nodes can differ widely at different scales. In particular, our measure correlates with degree (i.e., hubs) at small arXiv:1907.08624v1 [physics.soc-ph] 19 Jul 2019
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