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Abstract: We study the effects of spatial constraints on the structural properties ofnetworks embedded in one or two dimensional space. When nodes are embedded inspace, they have a well defined Euclidean distance $r$ between any pair. Weassume that nodes at distance $r$ have a link with probability $pr \sim r^{-\delta}$. We study the mean topological distance $l$ and the clusteringcoefficient $C$ of these networks and find that they both exhibit phasetransitions for some critical value of the control parameter $\delta$ dependingon the dimensionality $d$ of the embedding space. We have identified threeregimes. When $\delta 2d$ the networks are``large- worlds $l \sim N^{1-d}$ with high clustering. Our results indicatethat spatial constrains have a significant impact on the network properties, afact that should be taken into account when modeling complex networks.



Autor: Kosmas Kosmidis, Shlomo Havlin, Armin Bunde

Fuente: https://arxiv.org/







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