---- > [!definition] Definition. ([[node copying model for growing a DAG]]) > The **node copying model** for generating a [[network|directed]] [[acyclic network|acyclic graph]] proceeds as follows. For intuition, we use the language of citation networks. > Fix an [[degree|out-degree]] $c \in \mathbb{N}$. > >1. Initialize the [[network]] by instantiating $n_{0} > c$ nodes, each citing $c$ other nodes uniformly at random. [^1] >2. Hereon we add nodes one-by-one, each citing $c$ previous nodes. For each new node $\ell$ added we: > 1. Choose [[uniform random variable|uniformly at random]] a previous 'template' node $j$; > 1. Iterate over the bibliography of $j$. For each of its $c$ entries, we either > 1. With probability $\gamma$ copy that entry into the bibliography of $\ell$; > 2. With probability $1-\gamma$ add a citation to a node chosen uniformly at random from the entire [[network]]. > - So, $\ell$ is a 'mutated' version of $j$. > [!basicproperties] > - [[in-degree distribution of node copying model is power-law]] [^1]: Asymptotically speaking, it turns out that our choice of initial condition does not matter much. ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```