---- > [!definition] Definition. ([[density of a network]]) > The **density** of a [[simple graph|simple network]] $G$ with $n$ nodes and $m$ edges is defined to be $\rho :=\frac{m}{{n \choose 2}} =\frac{2m}{n(n-1)}=\frac{c}{n-1},$ > where $c$ denotes the [[mean degree]] of $G$. > \ > **Remark.** Note that $\rho \in [0,1]$. In can be thought of as the [[probability]] that a pair of nodes, picked uniformly at random from the whole [[network]], are connected. > [!justification] > This is just the number of edges in the [[network]] divided by the *possible* number of edges in the network (recall [[simple graph#^dcec5c|the number of edges in a fully-connected simple network is]] $n \choose 2$). ---- #### ---- #### 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 > ```