# directedEdgesMatrix -- matrix corresponding to the directed edges of a digraph or a mixed graph

## Synopsis

• Usage:
directedEdgesMatrix R
• Inputs:
• R, a ring, which should be a gaussianRing created with or an instance of the type MixedGraph
• Outputs:
• , the $n \times{} n$ matrix of direct causal effect indeterminates.

## Description

This method returns the $n \times{} n$ matrix of direct causal effect indeterminates. This matrix has the parameter $l_{(i,j)}$ in the $(i,j)$ position if there is a directed edge $i \to j$, and 0 otherwise. Note that this matrix is not symmetric. The documentation of gaussianRing further describes the indeterminates $l_{(i,j)}$.

 i1 : G = mixedGraph(digraph {{b,{c,d}},{c,{d}}},bigraph {{a,d}}) o1 = MixedGraph{Bigraph => Bigraph{a => {d}} } d => {a} Digraph => Digraph{b => {c, d}} c => {d} d => {} Graph => Graph{} o1 : MixedGraph i2 : R = gaussianRing G o2 = R o2 : PolynomialRing i3 : compactMatrixForm =false; i4 : directedEdgesMatrix R o4 = | 0 0 0 0 | | | | 0 0 l l | | b,c b,d | | | | 0 0 0 l | | c,d | | | | 0 0 0 0 | 4 4 o4 : Matrix R <--- R
 i5 : D = digraph{{a,b},{c,d}} o5 = Digraph{a => {b}} b => {} c => {d} d => {} o5 : Digraph i6 : directedEdgesMatrix gaussianRing D o6 = | 0 0 0 0 | | | | 0 0 l l | | b,c b,d | | | | 0 0 0 l | | c,d | | | | 0 0 0 0 | 4 4 o6 : Matrix R <--- R