---- > [!definition] Definition. ([[degree]]) > The **degree** $k_i$ of a node $k_{i}=\sum_{j=1}^{n}A_{ij}$ in an [[network|undirected network]] is the number of edges connected to it. > \ > The **out-degree** of a node in a [[network|directed network]] > \ > **Remark**. Every edge in an undirected network has two ends; thus if there are $m$ edges then there are $2m$ ends of edges. That is, $2m=\sum_{i=1}^{n}k_{i}=\sum_{i,j=1}^{n}A_{ij}.$[^1] ![[CleanShot 2023-09-12 at 22.00.52 1.jpg]] ---- #### [^1]: This is sometimes called the **handshaking lemma**. But only sometimes. ---- #### 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 > ```