---- > [!definition] Definition. ([[betweenness centrality]]) > Let $G$ be a [[network]] and $i$ a node in $G$. Let $n_{st}^{i}$ denote the number of [[geodesic distance in networks|shortest paths]] from $s$ to $t$ that pass through $i$, and let $g_{st}$ denote the total number of shortest paths from $s$ to $t$. Then the **betweenness centrality** of the node $i$ is given by $x_{i}:=\sum_{st, g_{st} \neq 0}^{} \frac{n^{i}_{st}}{g_{st}}.$ > > > [!note] Remark. [[Betweenness centrality]] [[centrality|is]] rather unique in that a node may have quite low [[degree]] but quite high [[betweenness centrality]]. ![[CleanShot 2023-09-24 at 19.25.43.jpg]] ---- #### ---- #### 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 > ``` #reformatrevisebbatch6