---- > [!definition] Definition. ([[tree]]) > A **tree** is a [[connected graph|connected]], [[network|undirected graph]] with no [[cycle|loops]]. > [!basicproperties] > - [[tree iff has n-1 edges]]; > - [[average degree of tree is strictly less than two]] > - Since trees have no closed loops, there is just one path between any two nodes. > [!basicexample] > - Many data structures are trees. Binary heaps are an example. > - Syntax trees for grammar (of both computer languages and natural languages). > - River [[network|networks]], save for the occasional island, are trees in the physical world. ---- #### ---- #### 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 > ```