---- > [!definition] Definition. ([[network]]) > A **graph** or **network** is a collection of nodes (or vertices) joined by edges. > \ > These edges can be **directed** or **undirected**. > \ Explicitly, an (undirected, simplicial) **graph** is the data of a pair $(\mathcal{V},\mathcal{E})$ where $\mathcal{V}$ is a set, whose elements are called nodes (or vertices) and $\mathcal{E} \subset \mathcal{P}(\mathcal{V})$ is a collection of subsets $\{ v,w \} \subset \mathcal{V}$ of size two; if $\{ v,w \} \subset \mathcal{E}$ then it is called an **edge** between $v$ and $w$. > [!note] Remark. > Sometimes the term **network** (or **complex network**) takes with it the connotation of "real world networks" (cf. CMPLXSYS 535). ^note ---- #### ---- #### 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 > ```