Circular plots are highly useful to visualize relationship between elements, like to show migration flow. The connections are drawn using the circos.link function. This function takes as input the origin and the destination of the link (element name, and zone of this element). You can custom the appearance of the link using lwd (thickness of border), lty (type of border), col (color), border (true or false) and h (shape of the link).

# library
library(circlize)

# Create data
set.seed(123)
data = data.frame(
    factor = sample(letters[1:8], 1000, replace = TRUE),
    x = rnorm(1000), 
    y = runif(1000)
    )

# Initialize the plot.
par(mar = c(1, 1, 1, 1) ) 
circos.initialize(factors = data$factor, x = data$x )

# Build the regions of track #1
circos.trackPlotRegion(factors = data$factor, y=data$y , bg.col = rgb(0.1,0.1,seq(0,1,0.1),0.4) , bg.border = NA)

# Add a link between a point and another
circos.link("a", 0, "b", 0, h = 0.4)

# Add a link between a point and a zone
circos.link("e", 0, "g", c(-1,1), col = "green", lwd = 2, lty = 2, border="black" )

# Add a link between a zone and another
circos.link("c", c(-0.5, 0.5), "d", c(-0.5,0.5), col = "red", border = "blue", h = 0.2)