---- > [!definition] Definition. ([[incidence matrix]]) > The **incidence matrix** of an [[network|undirected]], [[weighted network|unweighted]] [[bipartite graph]] with $n$ items and $g$ groups is a $g \times n$ [[matrix]] having elements $b_{ij}$ such that $b_{ij}=\begin{cases} 1 & \text{ if item } j \text{ belongs to group } i \\ 0 & \text{ otherwise.} \end{cases}$ > [!basicexample] > Consider the [[network]] below: > ![[CleanShot 2023-09-13 at [email protected]]] > Assuming filled nodes are 'items' and hollow nodes are 'groups', its **incidence matrix** is $\begin{bmatrix} 1 & 0 & 1 & 0 & 0 \\ 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 1 & 1 & 1 & 1. \end{bmatrix}$ ---- #### ---- #### 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 > ```