---- > [!definition] Definition. ([[simple graph]]) > When more than two edges connect a pair of nodes in a [[network|graph]], they are collectively called a **multiedge**. > \ > Edges that connect nodes to themselves are called **self-edges** or **self-loops**. > \ > A [[network|graph]] that has neither **self-edges** nor **multiedges** is called a **simple graph** or **simple network**. > [!basicproperties] > - If a [[simple graph]] has $n$ nodes, connected in a single component, then *at most* there are $(n-1)+(n-2)+\dots+1$ > edges (connect node 1 to each other node, connect node 2 to each node other than node 1, etc...). This is the sum of the first $n-1$ natural numbers; it equals $\frac{n(n-1)}{2}={n \choose 2}$. There are *at minimum* $(n-1)$ edges required (e.g., node 1 has one edge connecting it to node 2, node 2 has one edge connecting it to node 3, $\dots$, node $n-1$ has one edge connecting it to node $n$). ---- #### ---- #### 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 > ```