In ianmoran11/ralget: Algebraic graphs in R.

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.path = "man/figures/README-",
  out.width = "100%"
)

DAG operations of ralget are now in the raldag package.

ralget

Ralget creates and combines graphs with algebraic operations.

library(tidyverse)
library(tidygraph)
library(ggraph)
library(patchwork)
library(igraph)
library(magrittr)
library(ralget)

format <- theme(plot.title = element_text(hjust = 0.5)) +  theme(panel.background = element_rect(fill = rgb(.95,.95,.95,1),color = NA)) 
plotter <- function(graph, layout_df,title  ){
  graph %>% 
      ggraph(layout_df)  +
      geom_edge_link(
        aes(end_cap = circle(10, "pt"),
            start_cap = circle(10, "pt")),
        edge_colour = "black",
        arrow = arrow(
          angle = 15,
          length = unit(0.15, "inches"),
          ends = "last",
          type = "closed"
        )
      ) +
      geom_node_point(col = "grey66", size = 10, show.legend = FALSE) +
      geom_node_text(aes(label = name)) +
      theme_graph() + ggtitle(title) + format 
}

Combining Vertices

Take the following vertices:

p <- v("p") 
q <- v("q") 
s <- v("s") 
r <- v("r") 

The + operator places vertices in the same graph.
The * operator joins one vertex to another.

g1 <- p * q + s
g2 <- q * s + q* r
g3 <- s * r

g1 <- p*q+s
g2 <- q*s+q*r
g3 <- s*r
gg <- (g1+g2)
p1 <-
  g1 %>% 
  plotter(data.frame(x = c(1,2,2), y = c(2,2,1)),"g1 = p * q + s") +
  xlim(c(1,3))
p2 <-
  g2 %>% 
  plotter(data.frame(x = c(2,2,3), y = c(2,1,2)),"g2 = q * s + q * r") + 
  xlim(c(1,3))
p3 <-
  g3 %>% 
  plotter(data.frame(x = c(2,3), y = c(1,2)),"g3 = s * r") +
  xlim(c(1,3))
p1 + p2 + p3

Combining graphs

Overlaying graphs ( + )

The + operator overlays graphs.

gs <- (g1+g2)

g1 + g2

format <- theme(plot.title = element_text(hjust = 0.5)) +  theme(panel.background = element_rect(fill = rgb(.95,.95,.95,1),color = NA)) 
p1 <-
g1 %>%
    plotter(data.frame(x = c(1,2,2), y = c(2,2,1)),"g1") +
    xlim(c(1,3))
p2 <-
g2 %>%
    plotter(data.frame(x = c(2,2,3), y = c(2,1,2)),"g2") + 
    xlim(c(1,3))
p3 <-
gs %>%
    plotter(data.frame(x = c(1,2,2,3), y = c(2,2,1,2)),"g1 + g2") + 
    xlim(c(1,3))
p1 + p2 + p3

Connecting graphs ( * )

The * operator creates a link from each vertex in the first graph to each vertex in the second graph.

gp <- (g1*g3)

g1 * g3

p1 <-
g1 %>% plotter(data.frame(x = c(1,2,2), y = c(2,1.9,1)),"g1") + xlim(c(1,3))
p2 <-
g3 %>% plotter(data.frame(x = c(2,3), y = c(1,2)),"g2") + xlim(c(1,3))
p3 <-
gp %>% plotter(data.frame(x = c(1,2,2,3), y = c(2,1.90,1,2)),"g1 * g2")  
p1 + p2 + p3 + 
geom_edge_loop(end_cap = circle(10, "pt")) 

The Cartesian product ( %x% )

The %x% operator creates the graph product.

v0 <- v(name = "00") 
v1 <- v(name = "01") 
v2 <- v(name = "02") 
v3 <- v(name = "03") 
A <- v("A")
B <- v("B")
C <- v("C")
D <- v("D")
E <- v("E")
x = A*B+B*C+C*D+D*E+E*A
y = v0*v1+v1*v2+v2*v3

x %x% y

layout_df <-data.frame(
  x = c(-2.25625566239723, -2.06694404978908, -1.58402956895644, -1.55953811495272, -1.89737276852298), 
  y = c(0.138709465825545, -1.1508396186631, -0.585121176745636, 0.66449533913645, 1.38325400507676))
p1 <-  x %>% plotter(layout_df,"x") + xlim(c(-4,0))
layout_df <-data.frame( x = rev(c(1, 2, 3 ,4)), y = c(0, 0, 0,0)) 
p2 <-  (y) %>%  plotter(layout_df,"y")
p3 <- (x %x% y) %>% plotter("stress", "x %x% y") 
p1+ p2 + p3

Some more on vertices

Vertices are created with the v() function, which takes a name and list of attributes associated with the vertex. This creates a ralget/tidygraph object:

v("x", Latitude=  78.26077, Longitude=  -94.11077)

Edges

Edge attributes are added by interleaving e() between graph multiplication.

Here's a simple example:

v("X1") * e("E:X1.X2") * v("X2")

g <- v("X1") * e("E:X1.X2") * v("X2")

Installation

You can install the development version from GitHub with:

# install.packages("devtools")
devtools::install_github("ianmoran11/ralget")

ianmoran11/ralget documentation built on Oct. 12, 2023, 12:19 a.m.