Important:The networks package has been deprecated. Use the superseding command GraphTheory[IncidenceMatrix]instead.

This procedure returns the incidence matrix with rows representing vertices and edges representing columns.

If an edge is not incident to a vertex then the corresponding table entry is 0.  If a directed edge is leaving a vertex then the corresponding table entry is -1.  In all other cases,  the table entry is 1.

This routine is normally loaded via the command with(networks) but may also be referenced using the full name networks[incidence](...).

$\mathrm{with}\left(\mathrm{networks}\right)\:$

$G≔\mathrm{cycle}\left(4\right)\:$

$\mathrm{addedge}\left(\left[1\,3\right]\,G\right)\:$

$T≔\mathrm{incidence}\left(G\right)$

$T≔\left[\begin{array}{ccccc}1& 0& 0& 1& \mathrm{-1}\\ 1& 1& 0& 0& 0\\ 0& 1& 1& 0& 1\\ 0& 0& 1& 1& 0\end{array}\right]$

$T\left[1,2\right]$

$0$