hasse: Visualization of Hasse diagram specified by an adjacency matrix

Description

Given an adjacency matrix, this function displays the corresponding Hasse diagram. This is a wrapper function for graph creation using the Rgraphviz package.

Usage

hasse(e, v=NULL, elab="", ecol="black", ebg="gray", vcol="black", vbg="white", vsize=1, fvlab=".", fvcol="black", fvbg="white", fvsize=1, febg="black", fesize=1, main=paste("Hasse Diagram of", deparse(substitute(e))), compress=FALSE)

Arguments

An adjacency matrix, with $e_{i,j}$ indicating the edge size between vertices $i$ and $j$ ($e_{i,j} = 0$ means no edge between $i$ and $j$). The matrix must be rectangular with non-negative non-missing values.

Vector of names of the vertices. If null, the vertex names will be obtained from column names of adjacency matrix $e$.

elab

Labels of the edges. If it is a scalar value, all edges would have the same label. Otherwise, $elab$ must be a rectangular matrix (similar to adjacency matrix $e$). A value on $i$-th row and $j$-th column is a label of the edge between vertex $i$ and vertex $j$.

ecol

Edge label color. If scalar, all edge labels have the same color. Otherwise, $ecol$ must be in the form of adjacency matrix: a value on $i$-th row and $j$-th column is a color of the label of the edge between vertex $i$ and vertex $j$.

ebg

Edge line color. If scalar, all edges have the same color. Otherwise, $ebg$ must be in the form of adjacency matrix: a value on $i$-th row and $j$-th column is a color of the edge between vertex $i$ and vertex $j$.

vcol

Vertex label color. If scalar, all vertices have the same label color. Otherwise, $vcol$ must be a vector of the size corresponding to the number of vertices.

vbg

Vertex background color. If scalar, all vertices have the same background color. Otherwise, $vcol$ must be a vector of the size corresponding to the number of vertices.

vsize

Vertex sizes. If scalar, all vertices have the same size in the image. Otherwise, $vsize$ must be a vector of the size corresponding to the number of vertices.

fvlab

Labels of "dot" vertices. Must be scalar.

fvcol

"dot" vertex label color. Must be scalar.

fvbg

"dot" vertex background color. Must be scalar.

fvsize

"dot" vertex size. Must be scalar.

febg

Color of edges introduced by edge compression. Must be scalar.

fesize

Thickness of edges introduced by edge compression. Must be scalar and non-negative.

main

Main title of the diagram.

compress

TRUE if the edges should be compressed, i.e. if the maximum bi-cliques have to be found in the graph and replaced with a "dot" vertex. (See examples.)

Value

Nothing.

Details

This function depicts a Hasse diagram specified with an adjacency matrix $e$. Hasse diagram is a visualization of partially ordered set, by drawing its transitive reduction as an oriented graph. Each vertex corresponds to an element of the set. There is an edge between vertex $i$ and vertex $j$ iff $i < j$ and there is no $z$ such that $i < z < j$. The function is also capable of edge compression via introducing the "dot" edges: Let $U$, $V$ be two disjoint non-empty sets of edges, such that for each $u$ from $U$ and $v$ from $V$, there exists an edge from $u$ to $v$. (The number of such edges equals $|U| \cdot |V|$.) Starting from $|U| > 2$ and $|V| > 2$, the Hasse diagram may become too complicated and hence confusing. Therefore a compress argument exists in this function that enables ``compression'' of the edges in such a way that a new ``dot'' node $w$ is introduced and $|U| \cdot |V|$ edges between sets $U$ and $V$ are replaced with $|U|+|V|$ edges from set $U$ to node $w$ and from node $w$ to set $V$.

Examples

Run this code

  # linear order
  e <- matrix(c(0, 1, 1, 0, 0, 1, 0, 0, 0), nrow=3, byrow=TRUE)
  hasse(e)

  # prepare adjacency matrix
  m <- matrix(0, byrow=TRUE, nrow=5, ncol=5)
  m[3, 1] <- 1
  m[3, 2] <- 1
  m[4, 1] <- 9
  m[4, 2] <- 1
  m[5, 1] <- 1
  m[5, 2] <- 1
  m

  mc <- m
  mc[mc > 0] <- "red"
  ms <- m
  ms[ms > 0] <- "blue"

  # view m with default settings
  hasse(m, ebg="black")

  # view m WITHOUT edge compression and some fancy adjustments
  hasse(v=c("a", "b", "c", "d", "e"), 
             vcol=c(gray(0.5), gray(1), rep(gray(0), 3)), 
             vbg=gray(5:1/5), vsize=1:5, e=m, ecol=mc, ebg=ms, elab=m,
             compress=FALSE)

  # view m WITH edge compression and some fancy adjustments
  hasse(v=c("a", "b", "c", "d", "e"), 
             vcol=c(gray(0.5), gray(1), rep(gray(0), 3)), 
             vbg=gray(5:1/5), vsize=1:5, e=m, ecol=mc, ebg=ms, elab=m,
             compress=TRUE)