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• W2762936643 abstract "We present a general class of geometric network growth mechanisms by homogeneous attachment in which the links created at a given time $t$ are distributed homogeneously between a new node and the exising nodes selected uniformly. This is achieved by creating links between nodes uniformly distributed in a homogeneous metric space according to a Fermi-Dirac connection probability with inverse temperature $beta$ and general time-dependent chemical potential $mu(t)$. The chemical potential limits the spatial extent of newly created links. Using a hidden variable framework, we obtain an analytical expression for the degree sequence and show that $mu(t)$ can be fixed to yield any given degree distributions, including a scale-free degree distribution. Additionally, we find that depending on the order in which nodes appear in the network---its $textit{history}$---the degree-degree correlation can be tuned to be assortative or disassortative. The effect of the geometry on the structure is investigated through the average clustering coefficient $langle c rangle$. In the thermodynamic limit, we identify a phase transition between a random regime where $langle c rangle rightarrow 0$ when $beta < beta_mathrm{c}$ and a geometric regime where $langle c rangle > 0$ when $beta > beta_mathrm{c}$." @default.
• W2762936643 created "2017-10-20" @default.
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• W2762936643 date "2018-03-19" @default.
• W2762936643 modified "2023-10-15" @default.
• W2762936643 title "Geometric evolution of complex networks with degree correlations" @default.
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• W2762936643 doi "https://doi.org/10.1103/physreve.97.032309" @default.
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