ccgraph function

Cayley colour graph

A function to create and manipulate bipartite Cayley colour graphs

ccgraph(x, main=NULL, seed=0, maxiter=100, alpha=c(1, 1, 1), scope, loops, 
        collRecip, undRecip, showLbs, cex.main, conc, coord, clu, cex, lwd, 
        pch, lty, bwd, bwd2, att, bg, mar, pos, asp, ecol, vcol, vcol0, lbs, 
        col, lbat, swp, swp2, scl, mirrorX, mirrorY, mirrorD, mirrorL, mirrorV, 
        mirrorH, rot, hds, vedist, ffamily, fstyle, fsize, fcol, nr, gens, ...)

Arguments

• x: an algebraic structure, typically a "Semigroup" object class
• main: (optional) title of the plot
• seed: (optional) random seed number for the vertices' initial coordinates; ignored except for force, stress and rand
• maxiter: (optional) maximum number of iterations in layout algorithms; ignored except for force, stress and rand
• alpha: vector (vertex, edge, bg) with the alpha color transparency
• scope: (optional) scope of the graph (see details)
• loops: (optional, logical, and experimental) plot graph loops?
• collRecip: (optional and logical) whether or not collapse reciprocated edges in the undirected graph
• undRecip: (optional and logical) whether or not plot reciprocated edges as undirected
• showLbs: (optional and logical) whether or not show the vertex labels when dimnames available
• cex.main: (optional) size of the plot's title
• conc: (optional and logical) whether the layout is concentric or not
• coord: (optional) data frame with the coordinates of the vertices; if coordinates are given then the layout option is ignored
• clu: (optional) clustering of the vertices (see details)
• cex: (optional) size of the vertices
• lwd: (optional) width of the edges; ignored if valued is set to TRUE
• pch: (optional) symbol representing the vertices
• lty: (optional) shape of the edges
• bwd: (optional) width of the bundle edges. Ranges from 0 (edges collapsed) to the default 1 (depending on the vertices' size), and for valued a value greater than one is possible
• bwd2: (optional) width of the bundle loop edges.
• att: (optional) a vector or an array representing the vertex attributes
• bg: (optional) background color of the plot
• mar: (optional) margins of the plot
• pos: (optional) position of the vertices' labels (0 means ``at the center of the vertex'')
• asp: (optional) aspect ratio of the plot
• ecol: (optional) color of the edges
• vcol: (optional) color of the vertices
• vcol0: (optional) color of the vertices' contour (only works for pch 21 through 25
• lbs: (optional) vertex labels
• col: (optional) alias for vcol
• lbat: (optional) labels for the vertex attributes
• swp: (optional and logical) whether or not to swap the bundle patterns
• swp2: (optional and logical) whether or not to swap reciprocals
• scl: (optional and experimental) numerical scalar ($x$ and $y$) or vector ($x$, $y$) of the graph's scale
• mirrorX: (optional) mirror of the $X$ axis
• mirrorY: (optional) mirror of the $Y$ axis
• mirrorD: (optional) mirror reflection across diagonal $Y=X$
• mirrorL: (optional) mirror reflection across diagonal $Y=-X$
• mirrorV: same as mirrorX
• mirrorH: same as mirrorY
• rot: (optional) clockwise rotation of the graph in degrees
• hds: (optional and experimental) arcs' head scale
• vedist: (optional and experimental) a real number with vertex - edge distance
• ffamily: the font family
• fstyle: the font style
• fsize: the font size
• fcol: the font color
• nr: for conc layout, number of radii
• gens: (optional when absent) semigroup generators in x
• ...: Additional argument items (see e.g. par)

Details

The Cayley colour graph is a graphical representation of the relationships among relations in the relational structure of a given multiplex network. Both nodes and directed edges represent string relations, and each shape (and color) corresponds to a specific generator relation of the semigroup structure.

Returns

A plot of the semigroup or group structure.

Author(s)

Antonio Rivero Ostoic

See Also

semigroup, multigraph, frcd, conc

Examples

## Create an abstract semigroup from random data
arr <- round( replace( array(runif(18), c(3,3,2)), array(runif(18),
       c(3,3,2))>.5, 1 ) )

S <- semigroup(arr)

## plot semigroup's Cayley graph
ccgraph(S)