Dominator tree

Dominator tree of a directed graph.

dominator.tree (graph, root, mode = c("out", "in"))
A directed graph. If it is not a flowgraph, and it contains some vertices not reachable from the root vertex, then these vertices will be collected and returned as part of the result.
The id of the root (or source) vertex, this will be the root of the tree.
Constant, must be in or out. If it is in, then all directions are considered as opposite to the original one in the input graph.

A flowgraph is a directed graph with a distinguished start (or root) vertex $r$, such that for any vertex $v$, there is a path from $r$ to $v$. A vertex $v$ dominates another vertex $w$ (not equal to $v$), if every path from $r$ to $w$ contains $v$. Vertex $v$ is the immediate dominator or $w$, $v=\textrm{idom}(w)$, if $v$ dominates $w$ and every other dominator of $w$ dominates $v$. The edges ${(\textrm{idom}(w), w)| w \ne r}$ form a directed tree, rooted at $r$, called the dominator tree of the graph. Vertex $v$ dominates vertex $w$ if and only if $v$ is an ancestor of $w$ in the dominator tree.

This function implements the Lengauer-Tarjan algorithm to construct the dominator tree of a directed graph. For details see the reference below.


  • A list with components:
  • domA numeric vector giving the immediate dominators for each vertex. For vertices that are unreachable from the root, it contains NaN. For the root vertex itself it contains minus one.
  • domtreeA graph object, the dominator tree. Its vertex ids are the as the vertex ids of the input graph. Isolate vertices are the ones that are unreachable from the root.
  • leftoutA numeric vector containing the vertex ids that are unreachable from the root.


Domintor tree


Thomas Lengauer, Robert Endre Tarjan: A fast algorithm for finding dominators in a flowgraph, ACM Transactions on Programming Languages and Systems (TOPLAS) I/1, 121--141, 1979.

  • dominator.tree
## The example from the paper
g <- graph.formula(R-+A:B:C, A-+D, B-+A:D:E, C-+F:G, D-+L,
                   E-+H, F-+I, G-+I:J, H-+E:K, I-+K, J-+I,
                   K-+I:R, L-+H)
dtree <- dominator.tree(g, root="R")
layout <- layout.reingold.tilford(dtree$domtree, root="R")
layout[,2] <- -layout[,2]
if (interactive()) {
  plot(dtree$domtree, layout=layout, vertex.label=V(dtree$domtree)$name)
Documentation reproduced from package igraph, version 0.6.5-2, License: GPL (>= 2)

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