---- > [!definition] Definition. ([[projection of a bipartite network]]) > The (one-mode) **projection** of a [[bipartite graph]] is obtained by connecting two items together if they share the same group (or conversely). > [!basicproperties] > - [[bipartite graph projection's adjacency matrix is nearly gramian]] > [!basicexample] > ![[CleanShot 2023-09-13 at 18.10.47@2x 1.jpg]] > The **projection** of this network onto the upper ('filled') row of nodes is ![[CleanShot 2023-09-13 at [email protected]]], with [[adjacency matrix]] $\begin{bmatrix} 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 \\ 1 & 1 & 0 & 1 & 1 \\ 0 & 1 & 1 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \end{bmatrix}.$ > [!warning] > Projections are useful and widely employed, but their construction *discards* information present in the original [[bipartite graph]]. For example, a projection loses any information about how many groups two nodes share in common. ---- #### ---- #### 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 > ```